Introduction to Quantitative Research Methods_ An Investigative Approach.pdf

INTRODUCTION TO
QUANTITATIVE
RESEARCH METHODS

INTRODUCTION
TO QUANTITATIVE
RESEARCH
METHODS
A N I N V E S T I G A T I V E
APPROACH
M A R K B A L N A V E S a n d
P E T E R C A P U T I
SAGE Publications
London . Thousand Oaks . New Delhi

# Mark Balnaves and Peter Caputi 2001
Introduction # Alec McHoul 2001
First published 2001
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Contents
Acknowledgements xiii
Permissions xiv
1 Order at all Points: Counting and accounting 1
The Ql-Qt Continuum 1
Culture and the Reliability of `Data' 5
References 8
2 Starting the Inquiry: `But what happened then?' 10
Knowing What to Research 16
Exploration, Description and Explanation 16
Topics of Research 20
Knowing Whom to Research 21
Units of Analysis 21
Knowing How to Research 22
Literature Review 22
Secondary Analysis 25
Knowing When to Research 25
The Importance of Time 25
Research design 27
Summary 27
The Statistical Inquirer 29
Main Points 29
Review Exercises 30
References 31
3 De®ning the Inquiry: `Then how do you know?' 33
Tools of Methodology 34
Styles of Reasoning (deduction, induction and abduction) 36
Causality 40
Mapping Relationships 41
Tools of Measurement 44
What are Variables? 45
Operational Definitions 48
Contemporary Views on Measurement 50
Great Sociological Detective Stories:
Collecting Data Across Cultures: Can we measure cultural variation?
Culture's Consequences (Geert Hofstede) 51
Methodology and Theory 52
Method 53
Hypotheses and Operationalization 53
v

C O N T E N T S
Variables 55
Individualism and Masculinity 55
Power Distance 56
Uncertainty Avoidance 57
Summary 59
Main Points 61
Review Exercises 61
References 62
4 Methods of Inquiry: `It is a capital mistake to theorize before one
has data!' 64
Involvement and Method 65
Experimental Design 67
Different Types of Experimental Design 74
Survey Design 75
What is a Survey? 76
The Variable in Question 77
Nominal Variables/Questions 77
Ordinal Variables/Questions 78
Interval Variables/Questions 78
Ratio Variables/Questions 79
Multiple-Item Scales 79
Differential Scales 79
Cumulative Scales 80
Summative Scales 80
The Words in the Question 81
Administering the Questionnaire 84
Layout 84
Length of Questionnaire 85
Interview as Measurement 86
Validity 87
External Validity and Sampling 90
Population and Sampling Frame 91
Simple Random Sampling 91
Stratified Random Sampling 92
Multi-Stage Cluster Sampling 92
Sample Size 93
Non-Probability Sampling 95
Trade-Offs 95
Triangulation 95
Great Media and Politics Detective Stories:
Using Survey Data. Do media change people's political attitudes?
The People's Choice (Paul Lazarsfeld) 96
Methodology and Theory 97
Method 98
Hypotheses and Operationalization 98
Variables 100
vi

C O N T E N T S
Summary 103
Main Points 105
Review Exercises 106
References 106
5 `Data! Data! Data!': Analysing data from the inquiry 109
Looking at the Clues: The Statistical Sleuth 109
Why Explore Data? 110
Plotting Data 110
Stem and Leaf Displays 110
Example 5.1: Stem and leaf display 111
Histograms 113
Boxplots 115
Tables, Graphs and Figures 118
Does a Picture Always Paint a Thousand Words? Some issues with
representing data in graphical and tabular form 120
Using SPSS and Excel to Plot Data: Accounting for Tastes dataset 122
Methodology and Operationalization 123
Working with SPSS 124
Working with Excel 131
Describing Data 132
Numerical Summaries: What are they and why are they important? 132
Describing Location or Centrality 133
Some Notation 133
Example 5.2: Calculating the median of odd and even
numbered distributions 134
Mean vs Median (When is the evidence not contaminated?) 134
Describing Variability 135
Example 5.3: Calculating the variance of a set of values 137
Using SPSS and Excel to Describe Data 138
Working with SPSS 138
Working with Excel 140
Summary 142
Main Points 143
References 145
6 Finding Answers from the Inquiry: `Elementary, my dear Watson!' 147
Looking at Bivariate Data, Correlation and Regression 149
Plotting Bivariate Data 149
Correlation: a Measure of Co-Relation 151
Example 6.1: Computing the correlation coefficient 154
Introduction to Simple Linear Regression 156
Prediction and Correlation 156
Method of Least Squares 157
Example 6.2: Finding the regression line 159
Assessing the Fit of the Regression Model 160
Issue of Causation 161
vii

Using SPSS: Correlation and Regression 163
Using Excel 168
Looking at Categorical Data 171
Exploring Bivariate Categorical Data 171
Example 6.3: Computing the contingency coefficient 174
Inference: From Samples to Populations 175
Parameters, Estimates and Statistics 176
Sampling Distributions 177
Hypothesis Testing ± Don't just show me the evidence, convince me
that it is so! 180
One-Sample Tests 180
One-Sample Test for Categorical Data 183
Two-Sample Tests 185
Test of Equality of Means for Independent Samples 185
Example 6.4: t-test for independent samples 186
Rank Test for Independent Samples 189
Example 6.5: Rank test for two independent groups 190
Tests for Categorical Data 191
Tests for Related Samples 193
Rank Test for Correlated or Related Samples 195
Using SPSS and Excel: One-Sample Tests 196
Using SPSS and Excel: Two-Sample Tests 201
Introduction to Randomization Tests 211
Great Social Biology Detective Stories: `We must hunt for cases' 213
Is There An Ideal Person?: Quetelet, Galton, Pearson 214
Does a General Intelligence Factor Exist?:
Spearman and the introduction of correlation 215
Is There a Genetic Component to Intelligence?
Did Burt clone the data? ± data ain't always data!! 217
Are Social Factors More Important than Individual Inclinations?
Durkheim's study on suicide (The use of secondary data) 218
Summary 223
Main Points 224
References 227
7 Summarizing and Presenting Results: `Quite so!' 229
Reporting Empirical Research 232
Writing Style, Narrative Style 234
Detection and Deception 235
References 236
Appendix I: Sample Letter for Informed Consent 237
Appendix II: BSA Statement of Ethical Practice 239
Appendix III: The Statistical Inquirer 246
Index 249
C O N T E N T S
viii

Tables
Table 2.1 Impact of television on Western Samoan evening activities,
4±10 pm 20
Table 2.2 Time and research design 26
Table 2.3 Organizing a quantitative research study 28
Table 3.1 From construct to operational definition 54
Table 3.2 Actual questions used to construct individualism/masculinity
indexes 54
Table 3.3 Countries ranked by individualism scores 56
Table 3.4 Countries ranked by masculinity scores 56
Table 3.5 Countries ranked by power distance scores 57
Table 3.6 Countries ranked by uncertainty avoidance scores 58
Table 4.1 Effectiveness of Program A and B for men with initially
unfavourable and men with initially favourable attitudes 74
Table 4.2 Effectiveness of Program A and B for men of different
educational backgrounds 74
Table 4.3 Examples from Thurstone's differential scale 80
Table 4.4 Examples from Bogardus Social Distance scale 80
Table 4.5 Selected examples from Christie and Geis's Likert scale 81
Table 4.6 Sample questionnaire and coding column 86
Table 4.7 Rank order of French high school students' intelligence scores
obtained with three hypothetical measures 89
Table 4.8 Table of random numbers 92
Table 4.9 Random selection of households for interview 94
Table 4.10 Summary of sampling procedures 94
Table 5.1 Example of back-to-back plot 113
Table 5.2 Frequency distribution table for grouped data 114
Table 5.3 Hypothetical data for variables X and Y 117
Table 5.4 The anatomy of a table 120
Table 5.5 Mean ratings of intensity of emotion 122
Table 5.6 Reframed data: mean ratings of intensity of emotion 122
Table 5.7 Accounting for tastes: comparison of stratified sample with
official statistics 124
Table 6.1 Hypothetical data 149
Table 6.2 Hypothetical data on correlation between years of counselling
experience and effective outcome 154
Table 6.3 Data with outliers 156
Table 6.4 Distribution of votes by section 172

Table 6.5 Percentage of votes within each section 172
Table 6.6 A 2 2 contingency table 173
Table 6.7 Data for job performance and EC test 174
Table 6.8 Computational details for Table 6.7 175
Table 6.9 Some commonly used values from a set of normal tables 182
Table 6.10 Frequencies in colour and shape of peas 184
Table 6.11 Hypothetical data for number of successful free throws in two
conditions 185
Table 6.12 Descriptive statistics 187
Table 6.13 Frequencies relating to marital status and IQ 192
Table 6.14 Comparison of observed and expected frequencies for
Baller's data 192
Table 6.15 Hypothetical data for speech anxiety scores in two
conditions 194
Table 6.16 All possible permutations of six scores in two conditions 212
Table 6.17 Permutation distribution for data in Table 6.16 213
Table 6.18 Suicides in different countries per million persons of each
confession 220
Table 6.19 Influences of the family on suicide, unmarried men 221
Table 6.20 Influences of the family on suicide, unmarried women 221
Table 7.1 Example from Accounting for Tastes: combined music genre
preferences by gender 233
TA B L E S
x

Figures
Chart 1.1 Reports on Aboriginal youth and all youth-crime reports,
Feb. 1991 to Jan. 1992 3
Chart 1.2 News reports on Aboriginal youth-crime and all youth-crime
with actual crime data, Feb. 1991 to Jan. 1992 4
Figure 2.1 From assertions to evidence 23
Figure 3.1 Operationalization 48
Figure 4.1 Methods of data collection and personal involvement 65
Figure 4.2 Checklist for research design 66
Figure 4.3 Research methods and techniques of data collection 67
Figure 4.4 Basic experimental design 69
Figure 4.5 Different answering formats 84
Figure 4.6 Contingency questions 84
Figure 4.7 Factors affecting people's motivation to provide complete and
accurate information to the interviewer 87
Figure 4.8 Checklist for questionnaire design 88
Figure 4.9 Multi-stage cluster sampling ± following the census
tracts 93
Figure 4.10 Experimental choice based on issues of internal and external
validity 96
Figure 4.11 Whereas actual occupation does little to refine the relationship
between SES level and vote, it makes more difference whether
a voter considers himself as belonging to `business' or
`labour' 100
Figure 4.12 Religious affiliation splits the vote sharply 101
Figure 4.13 One-step model of mass-media influence 102
Figure 4.14 Two-step model of mass-media influence 102
Figure 4.15 Inductive approach 104
Figure 4.16 Deductive approach 104
Figure 5.1 A stem and leaf display of ESP data 114
Figure 5.2 Histogram of hypothetical examination marks 115
Figure 5.3 The anatomy of a boxplot 116
Figure 5.4 Boxplots for two hypothetical variables X and Y 117
Figure 5.5 Side-by-side boxplots 118
Figure 5.6 Preference for telecommunications carrier 121
Figure 5.7 A different way to display preference for telecommunications
carrier 121
Figure 6.1 Scatterplot for data in Table 6.1 150

Figure 6.2 Negative association between two variables 150
Figure 6.3 No relationship between two variables 151
Figure 6.4 Scatterplot showing an outlier 151
Figure 6.5 A curvilinear relationship 155
Figure 6.6 Fitting a line through points on a scatterplot 157
Figure 6.7 Illustrating the concept of residual 158
Figure 6.8 Bar chart of frequency of votes by selection 172
Figure 6.9 Bar chart of raw percentage of votes by selection 173
Figure 6.10 The normal distribution of a normal curve 179
Figure 6.11 The t-distribution 183
Figure 6.12 Durkheim's theoretical hypothesis on suicide 220
Figure 6.13 Durkheim's hypothesis of degree of integration 221
Figure 6.14 Durkheim's hypothesis of degree of regulation 222
F I G U R E S
xii

Acknowledgements
A special thanks to:
Gary Bouma and David DeVaus
Mark Busani, Nick Castle and Monica Vecchiotti for their help with the
multimedia courseware.
Maurice Dunlevy, for contributions on journalism, and Harry Oxley, for
contributions on causal diagramming.
Patrick Rawstorne for use of his PhD dataset Predicting and Explaining the
use of Information Technology with Value Expectancy Models of Behaviour
in Contexts of Mandatory Use.
Erika Pearson ± it's hard to find good help nowadays.
Tony Bennett, Mike Emmison and John Frow for use of their dataset from
The Australian Everyday Consumption project.
SPSS illustrations have been reprinted by SPSS copyright permission. Excel
illustrations have been reprinted by Excel copyright permission.
The Apple University Consortium and PCTech for their equipment and
software support.
The Australian National Library for assistance with access to The Strand,
from which the original Paget sketches of Sherlock Holmes were repro-
duced for this book.
Alec McHoul, Mike Innes, Joyce and Michele Balnaves, Wendy Parkins and
James Donald, who provided valuable insights into detection.
John and Paul Balnaves on questions of Shakespeare and logic.
Michele, Mary-Claire, Gerard, Elayne, James, and Jack.
Douglas Adams ± the bottle of red has been sent.
The authors of detective fiction.

Permissions
The authors and publishers wish to thank the following for their permission
to use copyright material:
Tables 6.16 and 6.17. Copyright # 1993. Canadian Psychological
Association. Reprinted with permission.
Page 12, extract from The Strange Crime of John Boulnois by G.K. Chesterton.
Used by permission of A.P. Watt on behalf of The Royal Literary Fund.
Page 14, extract from Dirk Gently's Holistic Detective Agency by Douglas
Adams. Used by permission of Douglas Adams. Copyright # 1987.
Heinemann.
Figure 2.1. From Evaluating Social Science Research, second edition, by Paul C.
Stern and Linda Kalof. Copyright # 1979, 1996. Oxford University Press,
Inc. Used by permission of Oxford University Press.
Table 2.2. Used by permission of Gary Bouma. Copyright # 1993. The
Research Process. Oxford University Press.
Page 38, extract from The Blue Cross by G.K. Chesterton. Used by permission
of A.P. Watt on behalf of The Royal Literary Fund.
Figure 4.3. Used by permission of David DeVaus. Copyright # 1990.
Surveys in Social Research. Allen and Unwin.
Table 4.7. From Research Methods in Social Relations, sixth edition, by Charles
M. Judd, Eliot R. Smith and Louise H. Kidder. Copyright # 1991, Holt,
Rinehart and Winston. Reproduced by permission of the publishers.
Every effort has been made to trace all copyright holders, but if any have
been overlooked, or if any additional information can be given, the publish-
ers will be pleased to make the necessary amendments at the first oppor-
tunity.

1
Order at All Points
Counting and accounting
A man is driving through the bush one day and has to stop while a farmer takes his sheep
across the road. There are quite a lot of sheep, so it takes a fair while. When they've all
passed by, the man goes up to the farmer and asks, Ìf I can tell you how many sheep you
have, to within one either way, can I have one of them?' The farmer replies, `Course you
can. You'll never get it right.' The man says, `You have six thousand four hundred and
twenty two.' `Well blow me down,' replies the farmer ± or words to that effect. Ìn fact I
have six thousand four hundred and twenty one. I counted them this morning.' So the man
walks back to the car with his prize.
`Wait on,' cries the farmer. Ìf I can tell you what your job is, can I have her back?' `Sure,'
says the man, `You'll never guess.' `Well,' says the farmer, Ì figure you'd be a statistician
with the Australian Bureau of Statistics.' `Well I'll be . . . !' the man replies, Èxactly right.
How on earth did you know that?'
The farmer comes back: `Put me dog down and I'll tell you.'
Traditional Australian Bush Yarn
THE Ql-Qt CONTINUUM1
Like many in the humanities and social sciences, I was trained to be (at the
least) sceptical about statistical methods and (at most) downright hostile
towards them. In sceptical mode, I was exhorted to use statistics not in the
way a drunk uses a lamppost: for support rather than illumination. In
hostile mode, the word was that statistics was for `positivists' (a very unfair
characterization, as it turns out, of positivism). What all of this well-mean-
ing and humanistic advice ignored was the sheer fact that our social and
cultural worlds, today, are massively subject to statistical accounts (see
Hacking, 1982). Whenever we turn on the TV news or open a newspaper,
the world is now routinely accounted for in terms of the numbers it gen-
erates: from world population statistics right down to chewing gum mar-
kets. In this respect, it's not quite as if numbers were on one side of the coin
and `lived cultures' on the other. Rather, the technologies of numbering
have become just one (though, in some disciplines, a dominant one) of
the many practices that make up the cultures of modernity. In this brief
introduction, then, I want to think through the supposed distinction (binary,
even) between the quantitative (Qt) and the qualitative (Ql) and to show
that the seal between the two is by no means as watertight as it is often
assumed to be.

My first realization of an elision between Qt and Ql came to me when, out
of sheer impecuniousness, I went to work for the Survey Research Centre at
the Australian National University (ANU) in the mid-1970s. Prior to this
way of supplementing my meagre PhD scholarship, my only encounter
with statistics had been the compulsory undergraduate methods course
in sociology, taught, as it happened, by a died-in-the-wool symbolic inter-
actionist, a Ql-man if ever there was one! Said lecturer was, then, very
happy for me to complete my statistics assignments by having a friend
who was a physics student crunch the exercises on the university's one
mainframe computer by submitting bundles of punchcards. Not, then,
exactly the best of trainings or qualifications, I admit. But working late at
ANU, designing and administering the Australian Capital Territory (ACT)
population surveys, I came to see what a symbolic and interactional process
Qt work could be in practice. One of our clients at the time was the local
Family Planning organization. It wanted to know which forms of contra-
ception were most in use in the Capital Territory. The only problem with
this was that the official sampling procedures required interviewers to
jointly interview two members of each household selected (using lot num-
bers) on a rotational basis: oldest and third oldest in odd-numbered lots,
and second oldest and fourth oldest in even-numbered lots. This meant, in
effect, that a fair proportion of interviews involved parents and their older
children ± not exactly the best interactional setting to ask people about their
contraceptive practices. The problem was both, and equally, statistical and
`cultural.' Qt and Ql could not be a simple binary. And, oh yes, the wonder-
ful `solution' we developed was to draw up a card with each kind of contra-
ception numbered. Respondents were then shown the card and would say
such things as `Well, I tried the number seven but it didn't work for me, so
now I prefer the twenty six.'
The same realization came back to me during a more recent research
project (Mickler and McHoul, 1998). In this project, we collected over 600
newspaper articles on Aborigines, youth and crime over a 12-month period
in the early 1990s in order to see whether there had been, as some suspected
at the time, a media-generated `crime wave.' We had a neutral reader/
research-assistant type the articles into a relational database program
(QSR NUDEIST) and, at the same time, code the articles for such things
as `source' (the origin of the reported events), `participants' (the categories
of persons reported on in each article) and how the reader thought the
article was treating such `participants' (in positive, negative or neutral
moral terms). What we hoped to get out of this was a strongly Ql argument
based on a discursive analysis of the news articles and their `readings.'
However, before long, we found that working with over 600 texts would
not allow us to do this. The data in question were simply too numerous.
And anyway, NUDEIST was starting to generate matrices of such things as
`Date of publication' `Article source' and `Newspaper' `Participants.'
Each cell of the matrix listed the relevant articles by their unique
NUDEIST document number. There was no way we could work with this
B A L N AV E S A N D C A P U T I
2

kind of output in a purely Ql mode. We had to show our findings graphi-
cally. This meant a lot of arduous work, transferring the totals of each cell
into an Excel spreadsheet and then having Excel generate graphs and bar
charts. (This was in NUDEIST version 3: the day we finished our gruelling
transcription work, NUDEIST 4 was released, including new software that
automatically converts such findings into popular spreadsheet and stats
programs.) At that point we were able to generate `findings' such as
those in Chart 1.1.
This was very useful to us because it showed us a picture of the year's
news in terms of just when the WA press was reporting youth crimes, and
the months during which young Aboriginal people were the `participants'
in those reports. However, while this could show us the media angle, it
could not tell us whether or not the `peaks' of youth crime reportage (and
we were particularly interested in the September peak because it followed
the infamous Rally for Justice outside Parliament House in the August)
corresponded to `actual' crime rates. If we were going to find a `media
wave,' we would have to overlay crime stats on to our bar chart. We even-
tually tracked these down at the University of Western Australia Crime
Research Centre whose staff kindly gave us their raw figures for the
12-month period in question. Accordingly we could then generate more
conclusive findings about the supposed `wave' ± see Chart 1.2.
O R D E R AT A L L P O I N T S
0
5
10
15
20
25
30
35
FEB
'91
MAR APR MAY JUNE JULY AUG SEP OCT NOV DEC JAN
'92
Date in Months
No.
of
News
Reports
Reports on Aboriginal Youth All Youth-Crime Reports
CHART 1.1 Reports on Aboriginal youth and all youth-crime reports, Feb.1991to Jan.1992
3

So we now had something like a `media wave.' That is, as the reportage of
youth crime peaked in September there was a corresponding decline in
`actual' crimes as measured by apprehensions and reports to the police.
Again, we could only see this graphically ± though later we resorted to a
more Ql discussion of how, in terms of routine media practices, the `wave'
could have been generated. That is, we wanted to show, from a close read-
ing of the reports (in line with well-known facts about the news profession
(Ericson et al., 1987, 1989, 1991)) that the statistically visible `wave' was not
so much a conscious conspiracy as a routine phenomenon in the field of
`bad news as usual.' As so frequently, the raw stats were open to more than
one interpretation and only one of these was that the media were `deliber-
ately' causing the appearance of a crime wave with possibly suspect and
populist motives.
Working on this project, then, brought me to the realization that there is in
fact a continuum between hypothetically `pure' Qt and Ql analysis. The
two, that is, never actually exist, empirically, in their pure states. Qt work
is part of the `culture' at large and Ql work is never strictly free of numbers.
So why then is there an effective stand-off between professionals in the two
methodological fields? Why do some Qt workers insist on accepted
sampling procedures and statistical reliability while some Ql workers
0
10
20
30
40
50
60
70
FEB '91 MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC JAN
'92
Date in Months
No.
of
News
Reports
(10=10),
No.
of
Apprehension
(10=100)
and
No.
of
Offences
Reported
to
Police
(10=1000)
Aboriginal Youth-Crime Reports
All Youth-Crime Reports
All Juvenile Apprehensions
Aboriginal Juvenile (Male) Apprehensions
Stolen Motor Vehicles, Break and Enter and Burglaries Reported to Police
(Crime Statistics Sources: Broadhurst and Ferrante (1995: 87); Broadhurst and Loh (1995: 72))
CHART 1.2 News reports on Aboriginal youth-crime and all youth-crime with actual crime data,
Feb.1991to Jan.1992
4

argue that very small fragments of cultural `data' (a poem, a few turns at
talk, an advertisement, and so on) can generate just as fruitful findings? In
order to begin to answer this question, we can turn to a rather extreme case
of an anti-Qt argument. The one I have in mind was mounted some years
ago by another major influence on my own methodological preferences:
Harvey Sacks.
CULTURE AND THE RELIABILITY OF `DATA'2
Just as in physics, natural phenomena must be massively sampled before an
argument about their properties can be mounted, so, in some branches of
the social sciences, cases must be sufficiently large in number before gen-
eralizations can be acceptable to the professional community. The parallel is
both noble and mistaken, according to several social theorists of (roughly)
a phenomenological persuasion. Alfred Schu
Ètz, many years ago, and in
works that are almost unknown to Qt types today, put this argument
very simply (Schu
Ètz, 1962: 34-47). He noticed that natural scientists deal
with objects of the first order of interpretation: that is, the objects that the
natural scientist has before her have not been interpreted until she herself
shows up on the scene. Atoms, planets and cyclones do not interpret them-
selves. However, as soon as we come to deal with human individuals or
populations, we're in a different situation entirely. These òbjects of know-
ledge' have interpreted themselves before the social scientist comes on the
scene. They are therefore òbjects' of the second order of interpretation. They
come pre-interpreted ± and so the job of anyone working in the human
sciences is to interpret the interpretations that people have already made
of their lives (individually) and their cultures (collectively). Where human
beings are concerned (as opposed to rats or atoms), the investigator is
always investigating `second order' matters. It is a fundamental category
mistake, then, to treat humanly produced data as `natural' data ± though,
as we will see shortly, this logical error need not preclude Qt analysis
altogether: I am simply taking this argument as one of the most cogent to
date on the underlying `philosophy' of much Qt thinking.
Sacks's important intervention into this debate ± possibly via his associ-
ation with Garfinkel (1967) who was, in turn, majorly influenced by Schu
Ètz
± is to argue for a unique position for cultural `data.' Not only, he ventures,
is culture distinct from nature, it also has unique orderly properties. That is:
in coming to analyse human cultures, one must take into account that they
display òrder at all points.' The argument is complex and students would
do best to consult the original (1995: 484). However, Schegloff (who intro-
duces both volumes) puts the matter succinctly. Accordingly, I quote at
length:
Considerations of enculturation and `language acquisition' provide an especially
provocative focus for a matter which Sacks raises . . . as a methodological point.
5

Taking up the relevance of sampling, Sacks points out that it depends on the sort
of order one takes it that the social world exhibits. An alternative to the possibility
that order manifests itself at an aggregate level and is statistical in character is
what he terms the òrder at all points' view. . . . This view, rather like the `holo-
graphic' model of information distribution, understands order not to be present
only at aggregate levels and therefore subject to an overall differential distri-
bution, but to be present in detail on a case by case, environment by environment
basis. A culture is not then to be found only by aggregating all of its venues; it is
substantially present in each of its venues. (Schegloff in Sacks 1995: xlvi)
As with holographs, a culture must display its inherent order, no matter
how much or little of it we happen to examine or `sample.' (And, as we will
see shortly, this importantly applies as much to the `much' as it does to the
`little.') Even if 99 per cent of a holographic image is destroyed, the remain-
ing 1 per cent contains all of the information contained in the original whole
(Roe, 1998). In this respect, when we are dealing with social and cultural
phenomena (such as `mental illness' or `suicide,' for example), the question
of whether we have sufficient cases for the `data' to be `reliable' may not
arise. The order we are seeking, as social scientists or cultural analysts,
according to Sacks, is not available as a form of statistical aggregation;
rather it must be inherently present in whatever materials happen to be
at hand ± for example just a few turns in a conversation. And, in fact,
Sacks directly uses his òrder at all points' (or ìn all venues') model to
criticize Qt research. His argument here is particularly directed at sociology
and survey research, but it applies equally well to the other social sciences:
. . . you might find that the fact of òrder at all points' could be used to explain
fairly strange facts; things like the following. For one, certain kinds of researches ±
for example, let's say, taking very conventional sociology, survey research ± would
use the fact that it gets orderly results to indicate that it must be doing something
decent. Now everybody knows ± that is, everybody who has ever done such work,
or studied it ± that it's almost universally extremely bad; that almost never can
whatever the constraints are that ought to be used under their own formulation to
decide that they have something, be used. There are, for example, all kinds of
constraints on proper statistical procedures which are never satisfied, and none the
less they get order. (1995: 484, my emphasis)
The argument here is important: the reason why Qt procedures arrive at
orderly outcomes may not be because of the `reliability' of either the sample
or the statistical techniques deployed on that sample. Rather, the order that
arises would be, for Sacks, an effect of the fact that, wherever a culture is
tapped into, and however frequently or infrequently it is sampled, it will
display its inherent order. If this is the case ± and I have yet to see a social
theory that directly defends an aggregationist model against the idea of
òrder at all points' ± then statistically reliable results may well be nothing
more than a case of something intrinsically non-statistical showing through
(and despite) the sampling techniques employed in any given case. The
6

consequences of such a `paradigm shift' are potentially massive for social
scientific thinking ± not least because they might change our thinking away
from what Wittgenstein (1958b: 18) called our `craving for generality' and/
or `the contemptuous attitude towards the particular case' (cf. Turner,
1974: 213).
However, none of this means that Qt work is without value.3
On the
contrary, as we have seen in our first section of this introduction, statistical
representations are sometimes inevitable: and in the above case, the reason
for this had to do with the necessarily longitudinal nature of the `media
wave' hypothesis. If this is so ± and because Ql and Qt exist on a continuum
and not as strict alternatives ± then even the most Ql-oriented researchers
will occasionally find themselves needing to use statistical models and their
ensuing graphic representations. If the `continuum' argument holds up
(and I think it does, at least from experience), then how can this live in
the same world as the òrder at all points' argument?
Sacks himself gives us the answer when he writes that, even when we do
proceed statistically, and even in its crudest form (the survey), we will find
the same cultural order as when we do not! `None the less they get order' is
precisely what he tells us. That is, if cultural `data' is intrinsically data of the
second order, any statistical analysis of it cannot help but preserve that aspect
of it. The `philosophy' of treating social and cultural phenomena as if they
were natural phenomena may well be a philosophical error ± associated
(probably wrongly) with `positivism.' But this does not mean that the
methods that flow from that error can somehow delete the orderly cultural
properties of the former kind of phenomenon. In fact, Sacks himself tells us
that they could not even if they wanted to.
This then sets the tone ± or more precisely, the ànalytic mentality'
(Schenkein, 1978) ± for the following chapters of this book.4
They introduce
some central social and cultural uses of Qt methods and, at the same time,
always remember the importance of the òrder at all points' that such
uses must bring out. Or to put this another way: there is no logical reason
why Qt methods can't be just as informed by a Sacksian view of cultural
order as they can by starting `positivistically' with physics envy. The result
is, I think, the first textbook in the field to bring cultural responsiveness
to statistical methods and, equally, statistical responsibility to cultural
analysis.
Alec McHoul
Murdoch University
6th January 2000
NOTES
1. This sub-title with apologies to Star Trek TNG. In many way, Star Trek's Q is the
ultimate detective. His case is nothing more or less than the human condition.
7

2. This section is based on parts of an article on Sacks, conversation analysis and
psychology by Alec McHoul and Mark Rapley (2000). For a good general intro-
duction to Sacks, see Silverman (1998).
3. For example, the foundational text of ethnomethodology, Garfinkel's Studies in
Ethnomethodology (1967), extensively uses statistical and quasi-statistical represen-
tations to show èxperimental' results.
4. I write `more precisely' with half an eye on the problem of what `precision' could
mean on the Ql±Qt continuum. To explain: the term ànalytic mentality' is from
Jim Schenkein (1978). He writes: Ì am never entirely sure of what I mean by
`ànalytic mentality'', but then goes on to say: Ì have come to think of [our] shared
practices [in conversation analysis] as ingredients in an `ànalytic mentality'' since
other more familiar terms fail to capture the spectrum of ingredients sketched
here. Our particular grouping of shared dispositions is not exactly a ``theory'' or
``method'', nor is it merely a ``point of view'' or some kind of ``philosophy''. But
whatever it is, the result is a research environment . . . and `ànalytic mentality'' is
fuzzy enough to embrace whatever comes up when a closer look at the environ-
ment is taken' (1978: 6). So this fuzzy formulation seems to be, paradoxically
perhaps, a more precise description than terms like `theory' and `method'. This
would be exactly my characterization of work that explicitly acknowledges and
works along the Ql±Qt continuum. As Wittgenstein (1958a: #71) puts it: Ìs it . . .
always an advantage to replace an indistinct picture by a sharp one? Isn't the
indistinct one often exactly what we need?'
REFERENCES
Broadhurst, Roderic and Ferrante, Anna (1995) `Trends in juvenile crime and justice,
1990±1992', in R. Harding (ed.) Repeat Juvenile Offenders: The Failure of Selective
Incapacitation in Western Australia. Nedlands, WA: Crime Research Centre,
University of Western Australia. pp. 79±95.
Broadhurst, Roderic and Loh, Nini Sui Nie (1995) `Selective incapacitation and the
phantom of deterrence', in R. Harding (ed.) Repeat Juvenile Offenders: The Failure of
Selective Incapacitation in Western Australia. Nedlands, WA: Crime Research Centre,
University of Western Australia. pp. 55±78.
Ericson, Richard, Baranek, Patricia and Chan, Janet (1987) Visualizing Deviance: A
Study of News Organization. Toronto: University of Toronto Press.
Ericson, Richard, Baranek, Patricia and Chan, Janet (1989) Negotiating Control: A
Study of News Sources. Stony Stratford: Open University Press.
Ericson, Richard, Baranek, Patricia and Chan, Janet (1991) Representing Order: Crime,
Law, and Justice in the News Media. Buckingham: Open University Press.
Garfinkel, Harold (1967) Studies in Ethnomethodology. Englewood Cliffs: Prentice-
Hall.
Hacking, Ian (1982) `Biopower and the avalanche of printed numbers', Humanities in
Society, 5 (3/4): pp. 279±95.
McHoul, Alec and Rapley, Mark (2000) `Sacks and clinical psychology', Clinical
Psychology Forum, 142 (August): pp. 5±12.
Mickler, Steve and McHoul, Alec (1998) `Sourcing the wave: Crime reporting,
Aboriginal youth and the WA Press, Feb 1991±Jan 1992', Media International
Australia incorporating Culture and Policy, 86 (February): pp. 122±52.
8

Roe, Phil (1998) Of Hologrammatology: The Politics of Virtual Writing. Unpublished
PhD thesis, Murdoch University.
Sacks, Harvey (1995) Lectures on Conversation, Vol. 1. Ed. G. Jefferson, intro. E.A.
Schegloff. Oxford: Blackwell.
Schenkein, Jim (1978) `Sketch of an analytic mentality for the study of conversational
interaction', In J. Schenkein (ed.) Studies in the Organization of Conversational
Interaction. New York: Academic Press. pp. 1±6.
Schu
Ètz, Alfred (1962) Collected Papers Vol. 1: The Problem of Social Reality. Ed. and
intro. M. Natanson. The Hague: Martinus Nijhoff.
Silverman, David (1998) Harvey Sacks: Social Science and Conversation Analysis.
Cambridge: Polity Press.
Turner, Roy (1974) `Words, utterances and activities', in R. Turner (ed.)
Ethnomethodology: Selected Readings. London: Penguin. pp. 197±215.
Wittgenstein, Ludwig (1958a) Philosophical Investigations. 2nd edn. Trans. G.E.M.
Anscombe. Oxford: Blackwell.
Wittgenstein, Ludwig (1958b) The Blue and Brown Books: Preliminary Studies for the
`Philosophical Investigations'. Oxford: Blackwell.
9

2
Starting the Inquiry
`But what happened then?'
`I'll tell you what happened then,' said Fiennes with a grim emphasis.
`When we got back into that garden the first thing we saw was Traill, the lawyer; I can see
him now with his black hat and black whiskers relieved against the perspective of the blue
flowers stretching down to the summer-house, with the sunset and the strange outline of
the Rock of Fortune in the distance. His face and figure were in shadow against the sunset;
but I swear the white teeth were showing in his head and he was smiling.
`The moment Nox saw that man the dog dashed forward and stood in the middle of the
path barking at him madly, murderously, volleying out curses that were almost verbal in
their dreadful distinctness of hatred. And the man doubled up and fled along the path
between the flowers.'
The Oracle of the Dog
Fiennes was a friend of Father Brown, G.K. Chesterton's famous priest-
detective. Fiennes was recounting a story to Father Brown about the reac-
tion of Nox, the dog, to a lawyer who represented Colonel Druce, a wealthy
man who had only recently been murdered. The newspapers had reported
that Druce had been murdered with a sharp knife in a garden with no
outside entry. The witnesses saw no murderer and there was no knife.
Fiennes thought that the dog's reaction to Traill the lawyer was a clear
sign that the lawyer was the murderer.
Father Brown, however, interrogates his friend further and discovers that
Colonel Druce changed his will and left his money to his daughter, rather
than to his son Harry Druce, who owed money from gambling. Harry
Druce committed suicide after his father's death. Father Brown also
found out that the dog had tried to retrieve something from the ocean on
a walk with Fiennes at the time of the murder and came back empty
handed. Father Brown comes to the conclusion that Colonel Druce, who
wore a white coat, was visible through a hedge that surrounded the garden.
A man with a walking-stick-knife had seen Druce through the hedge and
stabbed him. The man had then thrown the walking-stick-knife into the
ocean. The dog tried to retrieve the walking stick, but to no avail because
it sank. Harry Druce was the man who killed Colonel Druce. Harry killed
himself when he realized that his murder was in vain and that his severe
debts would not be resolved.
Fiennes is amazed that Father Brown can work out the crime from a
distance. Father Brown replies, `You asked how I could guess things a
hundred miles away but honestly it's mostly to your credit, for you

described people so well that I know the types.' Father Brown rejected
Fiennes's interpretation of the dog's reaction to Traill and instead broad-
ened the inquiry. Ì had a sort of guess,' said Father Brown, `right at the
beginning when you said that Druce wore a white coat.'
Father Brown was not a Columbo or a Hercule Poirot, who often as not
started their investigations knowing who the crook was. Father Brown
started his inquiries into mysterious unsolved crimes by collecting a wide
range of accounts and observations, no matter how zany or far fetched those
accounts and observations might superficially look. Father Brown did not
assume that the context of a crime was obvious and that knowledge of that
context came from looking at only a few clues. Father Brown carefully
weighs up what he has found (what he thinks is a clue) and the logical
consequences of what he has found (what he thinks must rationally follow).
In The Strange Crime of John Boulnois (Chesterton, 1987), Father Brown
arrives at a scene where an American journalist has witnessed the death
of Sir Claude Champion, dressed as Romeo and stabbed with a sword,
saying with his last breath `Boulnois . . . with my own sword . . . he threw
it . . .'. The journalist was on his way to interview John Boulnois, an Òxford
man' who had recently published a review on Darwinian evolution. Father
Brown interviews the wife of John Boulnois.
`Father Brown' she said.
`Mrs. Boulnois?' he replied gravely. Then he looked at her and immediately said: Ì
see you know about Sir Claude.'
`How do you know I know?' she asked steadily. [emphasis added]
He did not answer the question, but asked another: `Have you seen your hus-
band?'
`My husband is at home,' she said. `He has nothing to do with this.'
Again he did not answer; and the woman drew nearer to him, with a curiously
intense expression on her face.
`Shall I tell you something more?' she said, with a rather fearful smile. Ì don't
think he did it, and you don't either.'
Father Brown returned her gaze with a long, grave stare, and then nodded, yet
more gravely.
`Father Brown,' said the lady, Ì am going to tell you all I know, but I want you to
do me a favour first. Will you tell me why you haven't jumped to the conclusion of
poor John's guilt, as all the rest have done? Don't mind what you say: I±I know
about the gossip and the appearances that are against him.'
Father Brown looked honestly embarrassed and passed his hand across his fore-
head. `Two very little things,' he said. Àt least one's very trivial and the other
very vague. But such as they are, they don't fit in with Mr. Boulnois being the
murderer.'
He turned his blank, round face up to the stars and continued absent mindedly:
`To take the vague idea first. I attach a good deal of importance to vague ideas. All
those things that àren't evidence' are what convince me. [emphasis added] I think
a moral impossibility the biggest of all impossibilities. I know your husband only
slightly, but I think this crime of his, as generally conceived, something very like a
moral impossibility. Please do not think I mean that Boulnois could not be so
S TA R T I N G T H E I N Q U I R Y
1
1

wicked. Anybody can be wicked ± as wicked as he chooses. We can direct our
moral wills; but we can't generally change our instinctive tastes and ways of doing
things. Boulnois might commit a murder, but not this murder. He would not
snatch Romeo's sword from its romantic scabbard; or slay his foe on the sundial
as on a kind of altar; or leave his body among the roses; or fling the sword away
among the pines. If Boulnois killed anyone he'd do it quietly and heavily, as he'd
do any other doubtful thing ± take a tenth glass of port, or read a loose Greek poet.
No, the romantic setting is not like Boulnois. It's more like Champion.'
Àh!' she said, and looked at him with eyes like diamonds.
Ànd the trivial thing was this,' said Brown. `There were fingerprints on that
sword; fingerprints can be detected quite a time after they are made if they're
on some polished surface like glass or steel. These were on a polished surface.
They were half-way down the blade of the sword. Whose prints they were I have
no earthly clue; but why should anybody hold a sword half-way down? It was a
long sword, but length is an advantage in lunging at an enemy. At least, at most
enemies. At all enemies except one.'
Èxcept one!' she repeated.
`There is only one enemy,' said Father Brown, `whom it is easier to kill with a
dagger than a sword.'
Ì know,' said the woman. Òneself.'
There was a long silence, and then the priest said quietly but abruptly: Àm I right,
then? Did Sir Claude kill himself?'
`Yes,' she said, with a face like marble. Ì saw him do it.'
`He died,' said Father Brown, `for love of you?'
An extraordinary expression flashed across her face, very different from pity,
modesty, remorse, or anything her companion had expected: her voice became
suddenly strong and full. Ì don't believe,' she said, `he ever cared about me a rap.
He hated my husband.'
`Why?' asked the other, and turned his round face from the sky to the lady.
`He hated my husband because . . . it is so strange I hardly know how to say it . . .
because . . .'
`Yes?' said Brown patiently.
`Because my husband wouldn't hate him.'
Father Brown only nodded, and seemed still to be listening; he differed from most
detectives in fact and fiction in a small point ± he never pretended not to under-
stand when he understood perfectly well.
Mrs. Boulnois drew near once more with the same contained glow of certainty.
`My husband,' she said, ìs a great man. Sir Claude Champion was not a great
man: he was a celebrated and successful man. My husband has never been cele-
brated or successful; and it is the solemn truth that he has never dreamed of being
so. He no more expected to be famous for thinking than for smoking cigars. On all
that side he has a sort of splendid stupidity. He has never grown up. He still liked
Champion exactly as he liked him at school; he admired him as he would admire a
conjuring trick done at the dinner-table. But he couldn't be got to conceive the
notion of envying Champion. And Champion wanted to be envied. He went mad and
killed himself for that.'
(Used by permission)
Father Brown's detection style is summarized in his enigmatic comment
Àll those things that `àren't evidence'' are what convince me'. Father
12

Brown tries to avoid preconceived hypotheses and preconceived ideas
about the relevance of the things that he observes. Father Brown works
from ìnside out', carefully analysing all the events and clues (including
witness accounts) and then drawing conclusions based on the evidence.
In many of the Father Brown stories, of course, there is something Father
Brown knows that we do not know. We only find out at the end of the story
how Father Brown reached his conclusions and why. The detective's know-
ledge and the reader's knowledge are not always the same during a story.
For Father Brown and the reader, however, there are only a finite number of
interpretations of accounts available to explain the crime mystery. Indeed,
we would not want to read detective fiction if we thought that any story
accounted for what had happened.
If Father Brown works from the ìnside out' in his collection and analysis
of evidence, then Sherlock Holmes is perhaps the perfect example of the
detective who works from the òutside in'. Father Brown, like Holmes,
always held that there is a rational explanation for all things. Father
Brown, though, is seen as the inquisitive interviewer, collecting individual
facts and then solving the crime. Sherlock Holmes, in contrast, argued that
he could deduce the solution to the whole crime from only a few facts.
Holmes always enjoyed demonstrating his `powers of deduction' with Dr
Watson. Dr Watson recounts this scene from A Scandal in Bohemia.
One night ± it was on the twentieth of March, 1888ÐI was returning from a
journey to a patient (for I had now returned to civil practice), when my way led
me through Baker Street. As I passed the well-remembered door, which must
always be associated in my mind with my wooing, and with the dark incidents
of The Study in Scarlet, I was seized with a keen desire to see Holmes again, and to
know how he was employing his extraordinary powers. His rooms were bril-
liantly lit, and, even as I looked up, I saw his tall, spare figure pass twice in a
dark silhouette against the blind. He was pacing the room swiftly, eagerly, with his
head sunk upon his chest and his hands clasped behind him. To me, who knew his
every mood and habit, his attitude and manner told their own story. He was at
work again. He had risen out of his drug-created dreams and was hot upon the
scent of some new problem. I rang the bell and was shown up to the chamber
which had formerly been in part my own.
His manner was not effusive. It seldom was; but he was glad, I think, to see me.
With hardly a word spoken, but with a kindly eye, he waved me to an armchair,
threw across his case of cigars, and indicated a spirit case and a gasogene in the
corner. Then he stood before the fire and looked me over in his singular intro-
spective fashion.
`Wedlock suits you,' he remarked. Ì think, Watson, that you have put on seven
and a half pounds since I saw you.'
`Seven!' I answered.
Ìndeed, I should have thought a little more. Just a trifle more, I fancy, Watson.
And in practice again, I observe. You did not tell me that you intended to go into
harness.'
`Then, how do you know?'
13

Ì see it, I deduce it. [emphasis added] How do I know that you have been getting
yourself very wet lately, and that you have a most clumsy and careless servant
girl?'
`My dear Holmes,' said I, `this is too much. You would certainly have been
burned, had you lived a few centuries ago. It is true that I had a country walk
on Thursday and came home in a dreadful mess, but as I have changed my clothes
I can't imagine how you deduce it. As to Mary Jane, she is incorrigible, and my
wife has given her notice, but there, again, I fail to see how you work it out.'
He chuckled to himself and rubbed his long, nervous hands together.
Ìt is simplicity itself,' said he; `my eyes tell me that on the inside of your left shoe,
just where the firelight strikes it, the leather is scored by six almost parallel cuts.
Obviously they have been caused by someone who has very carelessly scraped
round the edges of the sole in order to remove crusted mud from it. Hence, you
see, my double deduction that you had been out in vile weather, and that you had
a particularly malignant bootslitting specimen of the London slavey. As to your
practice, if a gentleman walks into my rooms smelling of iodoform, with a black
mark of nitrate of silver upon his right forefinger, and a bulge on the right side of
his top-hat to show where he has secreted his stethoscope, I must be dull, indeed,
if I do not pronounce him to be an active member of the medical profession.'
I could not help laughing at the ease with which he explained his process of
deduction. `When I hear you give your reasons,' I remarked, `the thing always
appears to me to be so ridiculously simple that I could easily do it myself, though
at each successive instance of your reasoning I am baffled until you explain your
process. And yet I believe that my eyes are as good as yours.' [emphasis added]
`Then how do you know?', Watson asks Holmes. Ì see it, I deduce it', says
Holmes in reply. What made Holmes's explanations the superior ones, in
Watson's eyes, was the fact that Holmes could, in an apparently scientific
and law-like way, deduce so much about events from so few clues.
Sherlock Holmes and Father Brown differ in their detection styles but
both have to `give reasons' for their explanations. `Then how did you
know?' is a common refrain in detective fiction. Readers of detective fiction
would not be happy if their favourite detective gave conclusions without
reasons ± without justifications for what constituted evidence and how
evidence and conclusions fitted together.
But are there other styles of detection ± Flashes of insight? Sudden
guesses? Intuition? With no link to evidence at all?
Dirk Gently from Douglas Adams's Dirk Gently's Holistic Detective Agency
is a good example of a detective who is not interested in the accounts people
give him or in logical causal explanations of events. Dirk Gently's primary
concern is with the `fundamental interconnectedness of all things' ± thus the
`holistic' in the title of Gently's detective agency: `We solve the whole crime.
We find the whole person' (Adams, 1987: 111). Dirk Gently tries to solve
crimes with no reference to the logical connection between events, as in this
scene with his secretary Miss Pearce.
He thrust a piece of paper across the desk.
She picked it up and looked at it. Then she turned it round and looked at it again.
14

She looked at the other side and then she put it down.
`Well?' demanded Dirk. `What do you make of it? Tell me!'
Miss Pearce sighed.
Ìt's a lot of meaningless squiggles done in blue felt tip on a piece of typing paper,'
she said. Ìt looks like you did them yourself.'
`No!' barked Dirk, `Well, yes,' he admitted, `but only because I believe that is the
answer to the problem!'
`What problem?'
`The problem,' insisted Dirk, slapping the table, òf the conjuring trick!
I told you!'
`Yes, Mr Gently, several times. I think it was just a conjuring trick. You see them on
the telly.'
`With this difference ± that this one was completely impossible!'
`Couldn't have been impossible or he wouldn't have done it. Stands to
reason.'
Èxactly!' said Dirk excitedly. Èxactly! Miss Pearce, you are a lady of rare percep-
tion and insight.'
`Thank you, sir, can I go now?'
`Wait! I haven't finished yet! Not by a long way, not by a bucketful! You have
demonstrated to me the depth of your perception and insight, allow me to demon-
strate mine!'
Miss Pearce slumped patiently in her seat.
Ì think,' said Dirk, `you will be impressed. Consider this. An intractable problem.
In trying to find the solution to it I was going round and round in little circles in
my mind, over and over the same maddening things. Clearly I wasn't going to be
able to think of anything else until I had the answer, but equally clearly I would
have to think of something else if I was ever going to get the answer. How to break
this circle? Ask me how.'
`How?' said Miss Pearce obediently, but without enthusiasm.
`By writing down what the answer is!' exclaimed Dirk. Ànd here it is!' he slapped
the piece of paper triumphantly and sat back with a satisfied smile.
Miss Pearce looked at it dumbly.
`With the result,' continued Dirk, `that I am now able to turn my mind to fresh and
intriguing problems, like, for instance . . .'
He took the piece of paper, covered with its aimless squiggles and doodlings, and
held it up to her.
`What language,' he said in a low, dark voice, ìs this written in?'
Miss Pearce continued to look at it dumbly.
Dirk flung the piece of paper down, put his feet up on the table, and threw his
head back with his hands behind it.
`You see what I have done?' he asked the ceiling, which seemed to flinch slightly
at being yanked so suddenly into the conversation. Ì have transformed the
problem from an intractably difficult and possibly quite insoluble conundrum
into a mere linguistic puzzle. Àlbeit', he muttered, after a long moment of silent
pondering, àn intractably difficult and possibly insoluble one.'
He swung back to gaze intently at Janice Pearce.
`Go on,' he urged, `say that it's insane ± but it might just work!'
Janice Pearce cleared her throat.
Ìt's insane,' she said, `trust me.'
15

Dirk Gently sees a mystery where others do not. He provides meaningless
answers to that mystery. His secretary does not accept that there is a mys-
tery or the need for a solution. Ìt's insane', says Miss Pearce. This is of
course a part of the humour of this novel. Gently is an exaggerated example
of the role that `gut feelings', `guessing' and `lateral thinking' play in detec-
tive fiction. Guessing plays an important part in social science research, as
we will see later.
Dirk Gently, like Sherlock Holmes, believes that it is possible to explain
events by reference to `wholes' ± to interconnected laws that govern ± on the
surface ± seemingly unrelated events. Gently, like Holmes, held that if you
knew one link in the causal chain then you could find the `whole'. This
model of detection is similar to the `nomothetic' model in social science
research. A nomothetic model is a macro, probabilistic, approach to ana-
lysing what happens in society. The aim in the nomothetic model is to
identify general classes of actions or events in society and not to show all
the individual unique events that may lie behind them. The nomothetic
model of research is often contrasted with idiographic models in social
science, which analyse all the micro events behind a social phenomenon
(Babbie, 1986: 53±55). Father Brown's inquiries are idiographic in nature. He
looks at all the micro events associated with a murder mystery.
Both models of inquiry ± nomothetic and idiographic ± seek to explain
what is happening. Both models must be grounded in èveryday life'. The
art of the detective and the social scientist, of course, is in the ability to
identify important events and to explain the relationships between them.
Father Brown's question `But what happened then?' is the sign that an
inquiry ± an investigation ± has started. A good detective and a good social
scientist needs to know what, who, how and when to investigate. A good
social scientist needs a research design.
KNOWING WHAT TO RESEARCH
Exploration, Description and Explanation
In the murder mystery Cause of Death Dr Kay Scarpetta, a medical examiner
`detective', is called out to a strange drowning in a naval shipyard for
decommissioned naval ships and submarines. The first reaction of those
investigating the incident was that it was simply a drowning: `He probably
just drowned,' Green was saying. Àlmost every diving death I've seen was
a drowning. You die in water as shallow as this, that's what it's going to be'
(Cornwell, 1997: 14).
Scarpetta, however, avoids `closure' ± premature finishing of the case.
She takes the unusual step of diving to the body to investigate what has
happened ± to satisfy her own curiosity about what happened. She finds the
air hose tangled on the side of an old ship but decides that the diver could
have rectified this problem relatively easily. Scarpetta, after conducting the
16

postmortem, finds that there is also cyanide in the body. The murder mys-
tery gets more and more complex as the novel progresses, leading ulti-
mately to a major conspiracy to take over a nuclear power plant.
Scarpetta explores, describes and then explains what is happening. Social
science research sometimes involves all three kinds of research and some-
times only one. Exploratory research in social science is valuable when a
researcher wants to study a new area and/or to test methods, such as
surveys and survey questions, for investigating that area. Descriptive
research is one of the most common forms of research in social science
research. The census and surveys of public opinion are examples of descrip-
tive research. The census, for example, provides an overview of demo-
graphics (e.g. gender, income) of a whole population. Public opinion polls
show what people's voting intentions might be. A descriptive study may
raise issues that need explaining. Explanatory research, however, reports
not just `what is happening' but `why'. Let's look briefly at some descriptive
and explanatory studies on the sociology of news and the journalism pro-
fession.
In January 1993 John Henningham published preliminary findings from a
national survey of 1,068 Australian journalists, The Hack's Progress (1993: 45).
The composite picture of a journalist, he said,
is very different from the stereotype of middle-aged dissipation. The closer image
is a 1990s yuppie. The survey shows that the typical journalist is male, young, and
ambitious, with a middle-class, Anglo-Saxon background. There is an increasing
chance that the journalist had a tertiary education and is likely to be well paid,
content, committed to the career and optimistic about the future of the media. . . .
About 37 per cent say they are more likely to vote Labor, with 29 per cent Liberal
and 2 per cent National. The lean to the left is not a matter of background: most
journalists come from middle-class families, with fewer than three out of 10 from
blue-collar homes. Only one in 10 had parents in primary industry ± cause for
rural people to continue their complaints of limited and supposedly unsym-
pathetic coverage of their problems. The churches might also argue under repre-
sentation, with 74 per cent of journalists uninvolved in religion. Only 19 per cent
of journalists were born overseas and almost all of them came from an Anglo-
Celtic background. Fewer than 3 per cent of journalists are non-Caucasian.
Women hold one in three jobs, but this is an advance on the early 1970s, when the
ratio was one-in-10. Predictably, while 72 per cent of women say it is harder for
females to advance their careers, only 39 per cent of male journalists agree.
Women have an average of 27, against 37 for men. The combined median is 32,
young enough to explain some of the optimism found in the survey.
The most extensive national survey of journalists ever undertaken is that
done by Johnstone, Slawski and Bowman in the United States in 1971 and
published in 1976. They surveyed 1,313 journalists by telephone from a
national sample of 1,550. The authors estimate that fewer than half (45.7
per cent) of the 153,000 persons who reported themselves as `editors or
17

reporters' in the 1970 census were employed full-time in the American news
media.
They estimated the total full-time editorial manpower in English-
language news media in the United States at 69,500 and said that three-
quarters of them were employed in print media, about 20 per cent in broad-
cast media and about 5 per cent in wire services at the time of their survey.
More than half were employed by daily newspapers. Although they esti-
mated that freelancers might contribute up to 100,000 stories a week to the
news media, they did not include freelancers.
Johnstone, Slawski and Bowman found their 70,000 US journalists to be
overwhelmingly young, urban, mobile and male ± just as in Australia. They
also found that their journalists did not conform to the stereotype of hard-
drinking, callous and isolated creeps. In fact, they came from the same
social strata as those in charge of the economic and political systems.
There were few recruits from the working class.
Journalists did not have to have a degree to be a journalist but in fact 86
per cent of US journalists had attended college for one or more years, about
60 per cent were graduates and more than 18 per cent had done postgrad-
uate work. Although most studied journalism more than any other specific
subject, journalism majors were outnumbered by about 2 to 1 by persons
with other kinds of college training. The other subjects most in demand
were political science and government.
Johnstone, Slawski and Bowman's national survey of 1971 was replicated
in 1982±3 by David Weaver and Cleveland Wilhoit (1986). In the years
between 1971 and 1983 the USA had been involved in the Vietnam War,
All The President's Men had exposed the criminal behaviour of Nixon and his
aides in the White House, films such as Absence of Malice had questioned the
ethics of journalists, the American media had been faced with a series of
astronomical libel judgements, Janet Cooke had been awarded a Pulitzer
Prize for a Washington Post story which she had faked and public confidence
in the press had been eroded. Nevertheless, there was a 125 per cent
increase in journalism and mass communication enrolments between 1971
and 1985.
By 1983 there were an estimated 112,072 journalists in the United States.
Weaver and Wilhoit surveyed 1,001 of them. They found the typical journal-
ist to be a politically moderate, 32-year-old, college-educated, white
Protestant who earned $19,000 a year. The proportion of women had
increased from 20 per cent in 1971 to 34 per cent in 1983. Two out of
three journalists saw themselves as middle-of-the-road politically, 22 per
cent saw themselves as left of centre and 18 per cent to the right. This
was interesting because shortly before the Weaver and Wilhoit study was
published, Lichter, Rothman and Lichter published their survey of `elite'
journalists ± those working on 10 major news outlets ± and said one out of
two were left-of-centre, if the centre is defined as American businessmen.
Their journalists were more likely than the national sample to see their role
as challenging government. The Weaver and Wilhoit national sample were
18

more moderate: most saw their role as being `interpretive'. The next biggest
proportion saw their role as disseminating information. Only a small pro-
portion espoused the adversary role. In 1971, 58 per cent were college
graduates whereas in 1983, 70 per cent were and more than half of those
majored in journalism or communications. Generally, journalists earned less
in real dollars than they did in 1971. Most said they heard more about their
work from readers and viewers than from colleagues. When they studied
another sample of 1,400 journalists in the 1990s they found that journalists
had less autonomy than reported in the earlier studies and less job satisfac-
tion. The proportion of journalists planning to leave the profession was
double that of the 1983 studies. But the typical American journalist
remained a married white male in his thirties, with a bachelor's degree
(Weaver and Wilhoit, 1996).
Similar findings emerge from the British studies. In his Journalism
Recruitment and Training: Problems in Professionalization Oliver Boyd-Barrett
reports a 1969 survey of 99 trainee journalists in the two largest training
centres (1970: 181±201). More than half of them came from lower-middle
and upper-middle white-collar backgrounds and nine came from senior
executive±managerial±professional backgrounds. About half could qualify
for entrance to a university and he cites estimates that graduates comprise
from 6 to 15 per cent of the total intake of recruits to journalism each year.
Most (62 per cent) of those in his sample who were employed by news-
papers obtained their first job by writing letters on their own initiative to
one or several newspapers and another 25 per cent answered press adver-
tisements.
Boyd-Barrett's work also had an explanatory element. He investigated the
reasons for choosing journalism as a career: it was seen as a non-routine,
non-conventional, sociable occupation by 35 per cent of respondents; it was
the most desirable occupation available to 29 per cent; it was seen as cre-
ative by 16 per cent and more than 75 per cent wanted to write a book (a
novel in most cases); it was seen as self-educational by 5 per cent; as a
`bridging occupation' to a better job by 3 per cent; and as a public service
occupation by 1 per cent. In spite of the aspirations for the non-routine, non-
conventional and the creative, in practice the young journalists spent a
quarter or more of their work time at desk work or office work and most
of their outside work on covering routine, predictable events. Feature writ-
ing accounted for only 10 per cent of total time. Nevertheless, they felt little
dissatisfaction with the organization of their work or its opportunities. Most
of them wanted to go into feature writing, general reporting or special
writing which they saw as offering more opportunities for self-expression
and initiative.
Boyd-Barrett (1970: 60±4) says that most British recruits to journalism
begin on weekly provincial newspapers and that juniors made up about
two-fifths of the journalists on these papers in each of the years 1964±7.
Almost all start as general reporters and their first chance to specialize is
usually in sport. Although more than 60 per cent of national newspaper
19

journalists in Britain were over 35, the belief was widely held that `on your
35th birthday they push you down the rubbish chute'. It was also widely
asserted that many journalists were sacked but Tunstall (1970) could find
little evidence of this for the period 1965±8.
An understanding of the demographics of the journalism profession as
well as journalists' motivations for joining the profession combines descrip-
tive and explanatory aspects of social science research. The `what' of the
research and the `why' of the research overlap. In the surveys cited above
it is possible to gain an overview of who journalists are and to discover
trends in the journalism profession, including journalists' attitudes towards
journalism.
Topics of Research
Knowing what to research, knowing the purpose of the research, is key to
the first steps in a research design. Knowing whether the research is
exploratory, descriptive or explanatory is a part of knowing what to
research. The topics of social science research range from description ±
describing who the people or social groups are ± to explanation ± explaining
why those people or social groups think or behave the way they do.
Analysing how people or social groups think and behave includes ana-
lysis of attitudes, beliefs, personality traits and other factors associated with
motivation. Analysing how people or social groups behave includes ana-
lysis of the actual actions. Table 2.1, for example, tells us what is happening
with Western Samoan television behaviour, but it does not tell us why the
Samoans changed their behaviour. Why did they stop weaving mats? Was
television the cause?
What people do and what they say they do can also differ to a great
degree. In 1934 Lapiere travelled with a Chinese couple to 66 hotels, auto-
TABLE 2.1 Impact of television onWestern
Samoan evening activities, 4^10 pm
% of time spent
Without TV With TV
Prayers 6 4
Eating 17 10
Talking/Discussion 30 9
Story telling/Singing 15 3
Visiting friends/
Community activities 22 4
Playing cards/
Weaving mats 10 0
WatchingTV 0 70
Source: Martin (1987: 3^21)
20

mobile camps, tourist homes, and 184 restaurants and cafes in the United
States. The Chinese couple were accepted with open arms. Lapiere then sent
questionnaires to all the places he visited, asking them if they would accept
Chinese as guests. Ninety per cent replied `No' (Deutscher, 1973).
Detectives like the medical examiner Kay Scarpetta go through all the
steps of modern social science research. There is an exploratory element ±
seeing whether there is a suspicious death; there is a descriptive element ±
describing what actually happened to the dead person; and there is an
explanatory element ± the reasons for the person's murder by cyanide.
Scarpetta is interested in what people tell her but she is also interested in
the actual behaviour of the people she talks to.
Knowing what to research involves decisions on exploration, description
and explanation as well as decisions about the topic of the research itself.
These decisions will form part of a research design. Knowing whom to
research is also an important part of research design. Knowing whom is
not simply a matter of which people might be relevant to a study, but which
units of analysis.
KNOWING WHOM TO RESEARCH
Units of Analysis
Surveys on journalism as a profession involve individual journalists as the
unit of analysis ± each journalist is asked a question in a survey. The indi-
vidual journalist is also a member of a larger grouping ± the profession
itself. If we make the explanatory statement `educated men are more likely
than educated women to be journalists', then we are working at the level of
the individual as the unit of analysis. If we make the descriptive statement
that `the typical American journalist is a married white male in his thirties,
with a bachelor's degree', then we are also dealing with the individual as
the unit of analysis. However, if we said that journalists are more likely than
accountants to be tertiary educated, then we would be using the group as
the unit of analysis.
The social science researcher also has to decide who counts as a `journal-
ist'. This is especially important if we are drawing a `sample' of journalists
for investigation. We will deal with samples and populations later, but there
are important issues associated with the definition of a `journalist'. Is a
journalist anyone who belongs to the journalists' association or is it anyone
who writes a story for a publication (a local newsletter?). Is anyone who
runs their own website a journalist?
The `who' of research involves identifying the individuals who might be
relevant to a study and the social groups to which they belong. Sherlock
Holmes did this in his own way when he told Watson how he identified
him. `As to your practice, if a gentleman walks into my rooms smelling of
iodoform, with a black mark of nitrate of silver upon his right forefinger,
21

and a bulge on the right side of his top-hat to show where he has secreted
his stethoscope, I must be dull, indeed, if I do not pronounce him to be an
active member of the medical profession.'
In social science research it is essential that you identify what your unit
of analysis is. Is it criminals or crimes? Is it journalists or journalism?
Understanding your units of analysis forms part of your decisions on
research design. Poor definition of the unit of analysis and poor selection
of those units raise questions about the external validity of a study ± can the
results be generalized from a sample to all the units of analysis you are
studying? Your literature review will also help you to clarify the what and
the who of your study.
KNOWING HOW TO RESEARCH
Literature Review
Coming up with good topics in social science research is not easy.
Narrowing the topic ± giving it a decent focus and decent definition ± is
even more difficult. One of the most complex research topics this century
has been `Does media violence cause violent behaviour?' Popular concern
about the relationship between media and behaviour has been ongoing.
In 1993, international news agencies reported the murder of a four±year-
old English boy, James Bulger, by two 10-year-olds who kidnapped
him from a shopping centre and took him to a railway line. The four-
year-old suffered 30 blows inflicting 22 injuries to his head, another 20 to
his body. Bags containing 27 bloodstained bricks were also shown to
the jury together with a 22 kg railway bolt used in the attack. The 10-
year-old boys had watched over 300 adult violent videos in the previous
six months.
News media and the popular imagination often put media violence and
violent behaviour together in a causal relationship. But a causal relationship
has been difficult to measure. Social science research has swung backwards
and forwards from `no effect' to `powerful effects' and back again. Violent
video games are one of the latest research topics.
`Computer games don't trigger aggression: report', said The West
Australian, (December 4, 1999: 14). This five-year study, supported by the
Australian government, concluded that `Computer games do not promote
aggressive behaviour and are less disturbing for children than movies,
according to a new report. They are not addictive, nor do they ruin family
life, impair school performance or cause health problems' (Durkin and
Aisbett, 1999).
Cumberbatch and Howitt undertook a `state of the science' review of
media effects in 1989. They covered research into specific effects in areas
such as women and sex roles, race and racism, age and ageism, disable-
ment, alcohol, prosocial issues, sex and violence. Their conclusion was that
22

the `history of mass communication research is conspicuously lacking in
any clear evidence on the precise influence of the mass media. Theories
abound, examples multiply, but convincing facts that specific media content
is reliably associated with particular effects have proved quite elusive'
(Cumberbatch and Howitt, 1989: 25).
One of the reasons for the difficulty in establishing cause and effect,
according to Cumberbatch and Howitt, is that isolating the contribution
mass media make to problems such as violence is extremely difficult
because social perceptions about these phenomena are deeply embedded
and often difficult to define.
Lowrey and DeFleur (1983: 339) in their review of research argued that
there are three general possibilities which describe a possible relationship
between viewing media violence and aggressive behaviour:
1 The viewing of violence leads to aggressive tendencies.
2 Aggressive tendencies lead to the choosing of violence viewing.
3 Aggressive tendencies and the viewing of violence are both products of
some third condition or set of conditions.
Lowrey and DeFleur's conclusion is that `regular or frequent viewing of
violent television programs may cause aggressive behaviour' (1983: 341).
An analysis of other people's work, as the media and violence research
demonstrates, requires a critical eye. Stern and Kalof (1996), summarized in
Figure 2.1, provide a simple guide to checking `statements of fact' ± whether
statements constitute genuine evidence.
Some statements by authors are unsupported assertions. Simply saying
that media violence leads to violent behaviour is an unsupported assertion.
Simply referring to an author who says that media violence leads to violent
behaviour is certainly trying to support the statement, but it is an `appeal to
Unsupported
assertion
No
Is anything presented
as evidence? Appeal to Authority
Yes No
Casual observation
Were any observations
made about the facts? No
Yes
Were the observations
reliable? Yes
Evidence
FIGURE 2.1 From assertions to evidence (used by permission)
23

authority' rather than substantial evidence. If the author referred to has
substantiated his or her observations in a reliable manner, then we are
getting closer to evidence.
A literature review ± seeing what journal articles, books and other sources
say about previous and contemporary research on the topic ± is essential for
planning a research design. Like a compass, a literature review gives the
researcher a bearing on what has been done. It also assists conceptualization
and measurement in research design.
For example, violence as we all know is real, but how does a researcher
measure it? Sherman and Dominick (1986) attempted to measure the occur-
rence of violence in music videos. In their content analysis of violence in
music videos it was found that women, older adults and nonwhites are
more likely to be represented as aggressors than victims. `Aggressors and
victims were most likely to fall in the young adult age range (18±34).
Interestingly, older adults (35±54) were nearly twice as likely to be aggres-
sors as victims. For children, an opposite trend was noted: they were twice
as likely to be the targets as the agents of aggression' (1986: 86±87). The unit
of analysis in Sherman and Dominick's content analysis was the `concept
video'. For measurement of violence they used Gerbner's definition of a
violent act as an `overt expression of physical force with or without a
weapon, against self or other, compelling action against one's will on
pain of being hurt or killed or actually killing or hurting' (Gerbner, cited
in Sherman and Dominick, 1986: 83±4). Independent coders then categor-
ized aggressive and violent content by the type of violence (pushing,
punching, slapping, gunshot, etc.), whether the aggressor was an individual
or group, the sex, ethnic background and age of the victim, outcome of the
aggression (death, injury, no effect) and whether the violence was portrayed
realistically or unrealistically (1986: 84).
Your reaction to Sherman and Dominick's definition of `violence' might
be that it is too narrow ± surely there is emotional violence? psychological
violence? what about shouting? Once you start raising these types of ques-
tions you are querying the validity of the definitions being used ± the
construct validity and the internal validity of the study in question. These
are exactly the types of questions you should raise about definitions in
a study because it is these definitions that affect the measurement. Poor
definitions mean poor measurement.
The goal of a study should always be clearly stated. Spillman and
Everington (1989), for example, provided uncomplicated sentences to
describe their study: `The purpose of this study was to investigate whether
the thin image presented by media today is consistent with earlier body-
image stereotypes or whether current stereotypes are different. That is, is
this image now perceived by college students as possessing more desirable
characteristics?'
Spillman and Everington (1989) found in their literature review that
researchers have consistently reported stereotypical behavioural and
personality traits associated with each of the three different body-build
24

somatypes of endomorph, mesomorph and ectomorph. The most favour-
able traits have been assigned to the mesomorphic body build and the least
favorable to the ectomorphic and endomorphic builds. Their sample was
responses from 234 undergraduate students to a questionnaire. Each
student was asked to fill out a questionnaire of 10 questions describing
themselves (age, sex, weight range, height range, class, and school designa-
tion). The next 24 questions required an individual to assign a behavioural
characteristic to one of three female silhouettes. Spillman and Everington
(1989) found in their results that the very thin body image, the ectomorph,
was the most preferred somatype.
Secondary Analysis
Previous studies like Spillman and Everington's can be replicated ± done
again ± in different contexts or at different points in time ± to see what is
happening. Indeed, previous data can be re-analysed by other researchers.
This is called secondary analysis. The wealth of survey data in modern
societies, whether census, opinion poll, or other survey data, makes second-
ary analysis a common and economical method of research.
Secondary analysis may also form part of exploratory work in a study ±
for example identifying the characteristics of the people you are studying
from previous survey data. If the same methodology for collecting data has
been used over long periods of time, then useful comparison can be made.
Time is, indeed, an important factor in social science research design. A
thorough grounding in the literature ± the journal articles, books, reports
± associated with a research topic provides direction on how the research
might be conducted. Knowing when to research is also a critical dimension
of research design.
KNOWING WHEN TO RESEARCH
The Importance of Time
Sherlock Holmes, quite rightly, calls his work `cases'. They are case studies
that investigate `what is happening'. It is an investigation of one crime at a
particular point of time. Holmes's only long-term criminal investigation
involves his nemesis, Professor Moriarty ± the criminal genius.
Exploring, describing and explaining in quantitative social science
research requires a research design. Decisions on conceptualization, meas-
urement and who is to be researched also require a research design. Time is
important in a research design when the researcher wants to make compar-
isons. A simple case study involves looking at a single phenomenon at a
particular point in time. A longitudinal study involves investigating a
phenomenon or different groups over time, to see if there are any relevant
changes. For example, there have been changes in the demographics of the
25

journalism profession over time. Time is also relevant to experiments. An
experiment is a very controlled attempt to see whether specific independent
variables (assumed causes) are related to specific dependent variables
(assumed effects). The researcher tries to manipulate the environment in
an experiment to see what is happening. We will return to the idea of
`independent variables' in Chapter 3. Table 2.2 gives an overview of the
general options in research design.
Exploratory and descriptive research often use cross-sectional designs.
A British or US census, for example, is cross-sectional and describes the
population at a given point of time. Explanatory research can use cross-
sectional designs. A study designed to examine the influence of religious
affiliation on voting, for example, could be done at a particular point in
time. The problem with such `snapshot' research, if not replicated, is that it
cannot take into account changes over time. Longitudinal research solves
this problem by enabling comparison of the same groups and the same
phenomena over time. TV ratings, for example, involve the establishment
TABLE 2.2 Time and research design
Simple Case Study/Cross-Sectional Design
What's happening?
l
A
Longitudinal Study/Trends Studies/Panel Studies
Has there been a change in A over time?
l
A l
A
Time1 Time 2
Comparison
Are A and B different?
l
A
l
B
Longitudinal Comparison
Are A and B different over time?
l
A l
A
Time1 Time 2
l
B l
B
Time1 Time 2
Longitudinal Comparison
Are A and B different over time because of the independent variable?
Experimental Group
X (independent variable) öööö
l
A l
A
Time1 Time 2
Control Group l
B l
B
Time1 Time 2
Adapted from Bouma (1993:111). (Used by permission).
26

of `panels', thousands of households, that are monitored regularly by
ratings agencies.
RESEARCH DESIGN
We now have a rough checklist of the key elements of a research design.
Great ideas are important in social science research, just as they are in
detective fiction, but good ideas must be backed up by good design.
Good design assists not only the investigation but the administration of
quantitative research. It is very easy to underestimate the practical, admin-
istrative, side of organizing, collecting and analysing evidence. Table 2.3
outlines the key elements associated with research planning.
Many of the concepts in Table 2.3 have not yet been introduced, but they
do provide you with a roadmap to what is required. We will return to all the
major concepts as the book proceeds.
SUMMARY
Detectives try to make sense of what has happened, what is happening or
what is going to happen, in the world about them. They use different
methodologies and methods to make sense of, or add intelligibility to, the
evidence that faces them. They are also required to show how they came to
their conclusions and why one conclusion should be accepted rather than
another. Social science research, similarly, is public. It is required to demon-
strate its findings and to make itself open to critique and review.
There is the possibility of error in social science research. These errors can
be errors of human prejudice, errors of ego involvement (Holmes said he
tried to put prejudice aside); errors in observation (Watson was chastised
for not observing at all!); and premature closure of inquiry (Holmes was
scathing about police prejudging crimes, Scarpetta never closed off invest-
igations too quickly). There is also the possibility of overgeneralization
(Father Brown never made wild conclusions from the evidence).
The extracts from the works of Chesterton, Conan Doyle and Adams
show that different processes of reasoning and explanation occur in detec-
tive fiction. These processes of reasoning have their parallel in quantitative
research. Social scientists, like fictional detectives, have theories and hypo-
theses which they test against the evidence. They also have methods by which
they collect and analyse that evidence. Theories, hypotheses and methods
are integral to research and make research systematic.
Of course, there are different theories and different methods in social
science just as there are different styles of detection in fictional detective
novels. But common to all detective fiction, and social science, is the
requirement to explain what counts as evidence, and how conclusions fit
27

TABLE 2.3 Organizing a quantitative research study
PROBLEM
What is the goal of the research?
What is the problem, issue, or critical focus to be researched?
What are the important terms? What do they mean?
What is the significance of the problem?
Doyou want to test a theory?
Doyou want to extend a theory?
Doyou want to test competing theories?
Doyou want to test a method?
Doyou want to replicate a previous study?
Doyou want to correct previous research that was conducted in an inadequate manner?
Doyou want to resolve inconsistent results from earlier studies?
Doyou want to solve a practical problem?
Doyou want to add to the body of knowledge in another manner?
REVIEWOF LITERATURE
What does previous research reveal about the problem?
What is the theoretical framework for the investigation?
Are there complementary or competing theoretical frameworks?
What are the hypotheses and research questions that have emerged from the literature review?
SAMPLE
Who (what) will provide (constitute) the data for the research?
What is the population being studied?
Who will be the participants for the research?
What sampling technique will be used?
What materials and information are necessary to conduct the research?
How will they be obtained?
What special problems can be anticipated in acquiring needed materials and information?
What are the limitations in the availability and reporting of materials and information?
METHOD
What methods or techniques will be used to collect the data? (This holds for applied and non-applied
research)
What procedures will be used to apply the methods or techniques?
What are the limitations of these methods?
What factors will affect the study's internal and external validity?
Will anyethical principles be jeopardized?
DATA ANALYSIS
How will data be analysed?
What statistics will be used?
What criteria will be used to determine whether hypotheses are supported?
What was discovered (about the goal, data, method, and data analysis) as a result of doing preliminary work
(if conducted)?
CONCLUDING INFORMATION
How will the final research report be organized? (Outline)
What sources have you examined thus far that pertain toyour study? (Reference list)
What additional information does the reader need?
What time frame (deadlines) have you established for collecting, analysing and presenting data?
(Timetable)
Adapted from Rubin et al. (1990)
28

the evidence. Logical argument based on sound empirical evidence for
detectives and social scientists alike is superior to argument based on
false evidence, or no evidence at all. Social scientists are detectives. They
collect empirical evidence from the social world around them and make
decisions about that evidence. `Empirical research' in this case simply
means research based on evidence from the real world in contrast to theoretical,
which refers to ideas that are abstract or purely analytical. `A theory
remains theoretical until it is tested against the real world, with empirical
evidence' (McNeill, 1985: 2).
We will use the detective theme throughout this book on quantitative
methods. Quantitative methods and statistics in social science are about
logical inquiry. The different types of logic and the different types of
personality in detective fiction and social science are often the same. You
will find quirky characters in both types of detection, including the Dirk
Gently.
We will examine in depth the logic behind the styles of reasoning of
detectives like Father Brown and Sherlock Holmes and the nature of the
continuum between qualitative and quantitative. We will give examples of
famous detective stories of social science ± showing how inquiries were
started, investigated, and concluded. We will, finally, provide you with
some important tools of analysis ± basic statistics.
The Statistical Inquirer
The Statistical Inquirer multimedia courseware provided on the CD-ROM
introduces you to descriptive statistics. The step-by-step lessons cover the
library, the concept of variables, measures of centrality, variance, correlation
and regression, as well as the idea of statistical inference. These lessons are
designed to reinforce what is covered in this text. Short videos, using
LotusScreencam, provide a brief introduction to SPSS. A dataset from
Patrick Rawstorne's doctoral study on subjective computer anxiety,
Predicting and Explaining the use of Information Technology with Value
Expectancy Models of Behaviour in Contexts of Mandatory Use, has been
provided for practice. An Unsolved Mystery also gives you the opportunity
to test your basic statistics skills.
MAIN POINTS
. There is a logic to social science inquiry. Quantitative social scientific
inquiry requires evidence that is observable and testable. Researchers
must give explanations for their conclusions. Social science research is
public. This assists in avoiding bias in research.
. A research design is the guide to how the research was constructed and
carried out.
29

. Explanations in social science can be `nomothetic', dealing with the
larger contexts in which social phenomena occur, or ìdiographic', deal-
ing with unique events. `Data', however, is not `pregiven' in the social
sciences ± it is a part of processes of interpretation in society. Definitions
of `violence' are already affected, for example, by perceptions in society
of what violence is.
. Social science research can be exploratory, descriptive or explanatory.
Exploratory research is used for testing new ideas or areas of research
and/or testing methods used to collect data. Descriptive research, like
TV ratings, describes `what is' and provides an overview of a phenom-
enon. Explanatory research seeks to explain `why'. `Why' questions tend
to be theory questions.
. Units of analysis are part of `what is counted' in quantitative research.
This can be individuals or groups. It can also be items in a content
analysis of a newspaper or a video.
. A literature review is a preliminary investigation of what has been done
or what is being done in an area of study. It is essential to planning a
study. As you can see from the brief overviews of journalism as a pro-
fession and the relationship between media and effects, there is a sub-
stantial amount of existing research in these areas of study.
. Secondary analysis is an economical way of finding out new things from
existing data.
. Time is a major factor in developing a research design. Research can
be conducted once, at a particular point in time, or over time. Trend
studies and panels are longitudinal and allow comparison over time.
Experiments are the most controlled of all research studies, allowing
investigation of the impact of specific phenomena over a period of time.
REVIEW EXERCISES
1 Find two journal articles from a sociology, psychology or media
journal that you think are examples of descriptive and explanatory
research. Write a brief one-page summary of the research design.
2 Find a report on a research study in a newspaper, magazine or the
internet that you think uses unsupported assertions, appeals to
authority or casual observation (that do not appear to have been
tested).
3 Classify the following statements as either unsupported assertion,
appeal to authority, casual observation or evidence.
Ì never met a person I did not like'
Èveryone knows that smoking causes lung cancer'
Àccording to Rogers (1970) opinion leaders have extraordinary
influence over diffusion of innovations'
30

REFERENCES
Adams, D. (1987) Dirk Gently's Holistic Detective Agency. London: Heinemann.
Babbie, E. (1986) The Practice of Social Research. Belmont: Wadsworth.
Bouma, G.D. (1993) The Research Process. New York: Oxford.
Boyd-Barrett, O. (1970) `Journalism recruitment and training: problems in
professionalisation', in Jeremy Tunstall (ed.), Media Sociology. London:
Constable.
Chesterton, G.K. (1987) The Complete Father Brown: the enthralling adventures of fiction's
best-loved amateur sleuth. London: Penguin.
Cornwell, P. (1997) Cause of Death. London: Warner.
Cumberbatch, G. and Howitt, D. (1989) A Measure of Uncertainty: The effects of the
mass media. London: J. Libbey.
Deutscher, I. (1973) What We Say, What We Do: sentiments and acts. Glenview, IL: Scott,
Foresman.
Doyle, Arthur Conan (1952) The Complete Sherlock Holmes. Garden City, New York:
Doubleday.
Durkin, K. and Aisbett, K. (1999) Computer Games and Australians Today. Office of
Film and Literature Classification.
Henningham, J. (1981) `The television journalist: A profile', Media Information
Australia, 22: 5.
Henningham, J. (ed.) (1990) Issues in Australian Journalism. Melbourne: Longman
Cheshire.
Henningham, J. (1993) `The hack's progress', Time, 11 January: 45.
Henningham, J. (1996) `Australian journalists' views on professional associations',
Asia Pacific Media Educator (1): 144±52.
Hudson, W.J. (1964) `The education of a journalist in Australia', in E.L. French (ed.)
Melbourne Studies in Education 1963. Melbourne: Melbourne University Press.
pp. 321-47.
Hudson, W.J. (1964) `Status of the metropolitan daily journalist in Australia', The
Australian Journal of Social Issues, 2 (2).
Johnstone, J.W.C, Slawski, E.J. and Bowman, W.W. (1976) The News People: A
Sociological Portrait of American Journalists and Their Work. Urbana, IL: University
of Illinois Press.
Jones, R.L. and Swanson, C.E. (1954) `Small-city daily newspapermen: their abilities
and interests', Journalism Quarterly, 31: 38±55.
Judd, R.P. (1961) `The newspaper reporter in a suburban city', Journalism Quarterly,
38: 35-43.
Lichter, S.R., Rothman, S. and Lichter, L.S. (1986) Media Elite: America's new power-
brokers. Bethesda, MD: Ahler and Ahler.
Lowrey, S. and DeFleur, M.L. (1983) Milestones in Mass Communication Research. New
York: Longman.
Martin, A. (1987) `Media and social change ± with special reference to television',
Pacific Islands Communication Journal, 15 (1): 3±21.
McNeill, P. (1985) Research Methods. London: Tavistock.
Rubin, R.B., Rubin, A.M. and Piele, J. (1990) Communication Research: Strategies and
Sources (2nd edn). Belmont, CA: Wadsworth.
Sherman, B.L. and Dominick, J.R. (1986) `Violence and sex in music videos: TV and
rock `n' roll', Journal of Communication, 36 (1): 79±93.
31

Spillman, D. and Everington, C. (1989) `Somatypes revisited: have the media
changed our perception of the female body image?', Psychological Reports, 64:
887±90.
Stern, P.C. and Kalof, L. (1996) Evaluating Social Science Research. New York: Oxford.
Tunstall, J. (1970) Media Sociology. London: Constable.
Weaver, D.H. and Wilhoit, G.C. (1986) The American Journalist: A portrait of U.S. News
People and Their Work, Malwah, NJ: Lawrence Erlbaum.
Weaver, D.H. and Wilhoit, G.C. (1996) The American Journalist in the 1990s: U.S. News
People at the End of an Era. Malwah, NJ: Lawrence Erlbaum.
White, D.M. (1950) `The gatekeeper: a case study in the selection of news', Journalism
Quarterly, 27: 383±90.
32

3
Defining the Inquiry
`Then how do you know?'
`I never guess'
Sherlock Holmes, The Sign of Four
Sherlock Holmes realized that what often led the police of his day astray
was their tendency to adopt theories of a crime based on the wrong facts.
There is nothing more deceptive than an obvious fact, says Holmes.
`By an examination of the ground I gained the trifling details which I gave to that
imbecile Lestrade, as to the personality of the criminal.'
`But how did you gain them?'
`You know my method. It is founded upon the observation of trifles.' (The
Boscombe Valley Mystery)
Sherlock Holmes said that he did not guess. He relied on observations and
he had a method for analysing those observations. `Seeing' was not enough
for Holmes. Accurate observations were essential for his method.
'You see, but you do not observe [said Holmes to Watson]. The distinction is clear.
For example, you have frequently seen the steps which lead up from the hall to
this room.'
'Frequently.'
'How often?'
'Well, some hundreds of times.'
'Then how many are there?'
'How many? I don't know.'
'Quite so! You have not observed. And yet you have seen. That is just my point.
Now, I know that there are seventeen steps, because I have both seen and
observed.' (A Scandal in Bohemia)
Observations are the key to quantitative research methods. Measuring
observations is the task of quantitative research. But knowing that your
observations are quantifiable and constitute real evidence is no simple mat-
ter. In Chapter 2 we discovered that there is a range of ways of starting an
inquiry and designing a quantitative research study. We also found that
social scientists, like detectives, have different styles of reasoning about
evidence and what constitutes evidence. Finding a clue is one thing. But
making inferences, judgements, about the relevance of the clue is another

matter. Holmes's criticism of the police is based on his judgement that the
police not only missed the important clues but that their system for making
judgements about clues was also wrong. Holmes criticized police meth-
odology ± their science for finding out, as well as their method ± their
actual techniques for recognizing and collecting clues. In this chapter
we will explore the different styles of reasoning about evidence ± meth-
odology ± and the systems of measurement that have been developed
to quantify observations.
TOOLS OF METHODOLOGY
Holmes did not like theorizing ± trying to provide explanations ± without
data. He took detection to be about observed data, deduction and predic-
tion. His methods of detection, he said, were àn impersonal thing ± a thing
beyond myself'. The great consulting detective's methods of detection
entailed `severe reasoning from cause to effect' and, according to him,
were really the only notable feature about his cases. `Crime is common.
Logic is rare', said Holmes to Watson, berating his loyal partner for being
too sensationalist in his accounts of the different cases. Ìt is upon the logic
rather than upon the crime that you should dwell.'
Holmes said that àll life is a great chain, the nature of which is known
whenever we are shown a single link' (Study in Scarlet). If you think that this
statement sounds `nomothetic', then you are correct. Holmes's confidence
in his ability to show the `great chain' even extended to attempts to read the
train of thought of a person from their features, as was demonstrated to Dr
Watson in the story of the The Resident Patient.
It had been a close, rainy day in October. Our blinds were half-drawn, and Holmes
lay curled upon the sofa, reading and re-reading a letter which he had received by
the morning post. For myself, my term of service in India had trained me to stand
heat better than cold, and a thermometer of ninety was no hardship. But the paper
was uninteresting. Parliament had risen. Everybody was out of town, and I
yearned for the glades of the New Forest or the shingle of Southsea. A depleted
bank account had caused me to postpone my holiday, and as to my companion,
neither the country nor the sea presented the slightest attraction to him. He loved
to lie in the very centre of five millions of people, with his filaments stretching out
and running through them, responsive to every little rumour or suspicion of
unsolved crime. Appreciation of nature found no place among his many gifts,
and his only change was when he turned his mind from the evildoer of the town
to track down his brother of the country.
Finding that Holmes was too absorbed for conversation, I had tossed aside the
barren paper, and, leaning back in my chair I fell into a brown study. Suddenly my
companion's voice broke in upon my thoughts.
'You are right, Watson,' said he. Ìt does seem a very preposterous way of settling a
dispute.'
34

'Most preposterous!' I exclaimed, and then, suddenly realizing how he had
echoed the inmost thought of my soul, I sat up in my chair and stared at him
in blank amazement.
'What is this, Holmes?' I cried. `This is beyond anything which I could have
imagined.'
He laughed heartily at my perplexity.
'You remember,' said he, `that some little time ago, when I read you the passage in
one of Poe's sketches, in which a close reasoner follows the unspoken thoughts of
his companion, you were inclined to treat the matter as a mere tour de force of the
author. On my remarking that I was constantly in the habit of doing the same
thing you expressed incredulity.'
'Oh, no!'
'Perhaps not with your tongue, my dear Watson, but certainly with your eye-
brows. So when I saw you throw down your paper and enter upon a train of
thought, I was very happy to have the opportunity of reading it off, and even-
tually of breaking into it, as a proof that I had been in rapport with you.'
But I was still far from satisfied. `In the example which you read to me,' said I, `the
reasoner drew his conclusions from the actions of the man whom he observed. If I
remember right, he stumbled over a heap of stones, looked up at the stars, and
so on. But I have been seated quietly in my chair, and what clues can I have
given you?'
'You do yourself an injustice. The features are given to man as the means by which
he shall express his emotions, and yours are faithful servants.'
'Do you mean to say that you read my train of thoughts from my features?'
'Your features, and especially your eyes. Perhaps you cannot yourself recall how
your reverie commenced?'
'No, I cannot.'
'Then I will tell you. After throwing down your paper, which was the action which
drew my attention to you, you sat for half a minute with a vacant expression. Then
your eyes fixed themselves upon your newly framed picture of General Gordon,
and I saw by the alteration in your face that a train of thought had been started.
But it did not lead very far. Your eyes turned across to the unframed portrait of
Henry Ward Beecher, which stands upon the top of your books. You then glanced
up at the wall, and of course your meaning was obvious. You were thinking that if
the portrait were framed it would just cover that bare space and correspond with
Gordon's picture over there.'
'You have followed me wonderfully!' I exclaimed.
'So far I could hardly have gone astray. But now your thoughts went back to
Beecher, and you looked hard across as if you were studying the character in
his features. Then your eyes ceased to pucker, but you continued to look across,
and your face was thoughtful. You were recalling the incidents of Beecher's career.
I was well aware that you could not do this without thinking of the mission which
he undertook on behalf of the North at the time of the Civil War, for I remember
you expressing your passionate indignation at the way in which he was received
by the more turbulent of our people. You felt so strongly about it that I knew you
could not think of Beecher without thinking of that also. When a moment later I
saw your eyes wander away from the picture, I suspected that your mind had
now turned to the Civil War, and when I observed that your lips set, your eyes
sparkled, and your hands clinched, I was positive that you were indeed thinking
of the gallantry which was shown by both sides in that desperate struggle. But
D E F I N I N G T H E I N Q U I R Y
35

then, again, your face grew sadder; you shook your head. You were dwelling
upon the sadness and horror and useless waste of life. Your hand stole towards
your own old wound, and a smile quivered on your lips, which showed me that
the ridiculous side of this method of settling international questions had forced
itself upon your mind. At this point I agreed with you that it was preposterous,
and was glad to find that all my deductions had been correct.
'Absolutely!' said I. `And now that you have explained it, I confess that I am as
amazed as before.'
'It was very superficial, my dear Watson, I assure you. I should not have intruded
it upon your attention had you not shown some incredulity the other day. But the
evening has brought a breeze with it. What do you say to a ramble through
London?'
Sherlock Holmes did not have to talk to Watson to discover his thoughts and
intentions. He could, he said, infer the thoughts, and their sequence, from
specific non-verbal events. What strikes us with Holmes is his emphasis on
cause and effect, and the treatment of his observations and deductions as
though they were scientific. Indeed, Holmes is the epitome of the scientific
detective. He wrote an article for a magazine about science and deduction
called `The Book of Life' and a monograph outlining his scientific method
called Upon the Distinction Between the Ashes of the Various Tobaccos: An
Enumeration of 140 Forms of Cigar, Cigarette and Pipe Tobacco, with Coloured
Plates Illustrating the Differences in the Ash. It is precisely the scientific side of
the cocaine-snorting Holmes that made him a hero of 19th and 20th century
readers.
Styles of Reasoning (deduction, induction and abduction)
Holmes's reading of Watson's thoughts, however, is not, in fact, deduction.
It is, in fact, a case of abduction, or guessing, as Umberto Eco (1983: 216), who
wrote his own detective novel The Name of the Rose, has pointed out. `Watson
threw down his paper and then fixed the picture of General Gordon. This
was undoubtedly a fact. That afterward he looked to another (unframed)
portrait was another fact. That he could have thought of the relation
between these two portraits can be a case of undercoded abduction,
based on Holmes's knowledge of Watson's interest in interior decoration.
But that, from this point on, Watson thought of the incidents of Beecher's
career was undoubtedly a creative abduction . . . Holmes invented a story. It
simply happened that that possible story was analogous to the actual one.'
Holmes, in short, guessed, but what is appealing to the reader is the fact
that he guessed so well. For Eco, Holmes was `meta-betting' ± betting that
the `possible world' he has outlined ± his guess ± is the same as the `real
one' ± Watson's actual thoughts. There is an important difference between
Eco and Holmes on this point. Holmes thinks that his inferences ± his
deductions ± about his observations can be referred back to a `great
chain' of causes and effects. Eco is saying that Holmes's guesses are not
deductions.
36

Umberto Eco introduces the idea of undercoded abduction, which is, for all
intents and purposes, the old idea of induction. He also uses the idea of
overcoded abduction, which is the old idea of deduction. Creative abductions
(or meta-abductions) for Eco are the big guesses. Detectives bet by meta-
abduction, scientists test their abductions.
What Watson's account shows us is that Holmes used different kinds of
logic ± and guessing was one of them. For Holmes, all knowledge is derived
from hypotheses, but a hypothesis is not always fully tested. Holmes in-
directly acknowledges the more dangerous nature of hypothesis when he
advocates the use of ìmagination' (The Retired Colourman, Silver Blaze),
ìntuition' (The Sign of Four) and `speculation' (Hound of the Baskervilles).
Holmes is referring here to what C.S. Peirce called àbduction' or
`retroduction'.
Abduction makes its start from the facts, without, at the outset having any par-
ticular theory in view, though it is motivated by the feeling that a theory is needed
to explain the surprising facts. Induction makes its start from a hypothesis which
seems to recommend itself, without at the outset having any particular facts in
view, though it feels the need of facts to support the theory. Abduction seeks a
theory. Induction seeks for facts. In abduction the consideration of the facts sug-
gests the hypothesis. In induction the study of the hypothesis suggests the experi-
ments which bring to light the very facts to which the hypothesis had pointed
(cited in Sebeok and Umiker-Sebeok, 1983: 25).
Peirce described the formation of a hypothesis as àn act of insight', the
àbductive suggestion' coming to us `like a flash' (cited in Sebeok and
Umiker-Sebeok, 1983: 18). Abduction, for Peirce, is the first step of scientific
reasoning, an instinct which relies upon unconscious perception of connec-
tions between aspects of the world, or to use another set of terms, sublim-
inal communication of messages.
Eco outlines the difference between deduction and induction using an
account from C.S. Peirce:
I once landed at a seaport in a Turkish province; and as I was walking up to the
house which I was to visit, I met a man upon horseback, surrounded by four
horsemen holding a canopy over his head. As the governor of the province was
the only personage I could think of who would be so greatly honored, I inferred
that this was he. This was an hypothesis. (cited in Eco, 1983: 219)
Eco says that C.S. Peirce made two inferences. The first one was a hypo-
thesis or deduction ± he knew the general rule according to which a man with
a canopy over his head, in Turkey, could not be anybody but an authority,
and imagined that the man he met represented a case of that unquestion-
able rule. The second one was an inductive inference: of the various au-
thorities that could have been in that place (why not a visiting minister
from Istanbul?), the governor of the province was the most plausible.
37

The importance of the role of different styles of reasoning is often expli-
citly highlighted in detective fiction. In G.K. Chesterton's The Blue Cross
(1987) the great French police detective Valentin is trying to track down
Flambeau, a brilliant crook who, disguised as a priest, is travelling with
Father Brown and planning to steal a valuable cross from him. Valentin
resorted to guessing ± abduction ± when traditional `logic' did not appear
to be appropriate.
Exactly because Valentin understood reason, he understood the limits of reason.
Only a man who knows nothing of motors talks of a motoring without petrol;
only a man who knows nothing of reason talks of reasoning without strong,
undisputed first principles. Here he had no strong first principles. Flambeau
had been missed at Harwich; and if he was in London at all, he might be anything
from a tall tramp on Wimbledon Common to a tall toastmaster at the Hotel
Metropole. In such a naked state of nescience, Valentin had a view and a method
of his own.
In such cases he reckoned on the unforeseen. In such cases, when he could not
follow the train of the reasonable, he coldly and carefully followed the train of the
unreasonable. Instead of going to the right places ± banks, police-stations, rendez-
vous ± he systematically went to the wrong places; knocked at every empty house,
turned down every cul de sac, went up every lane blocked with rubbish, went
round every crescent that had him uselessly out of the way. He defended this
crazy course quite logically. He said that if one had a clue this was the worst way;
but if one had no clue at all it was the best, because there was just the chance that
any oddity that caught the eye of the pursuer might be the same that had caught
the eye of the pursued.
Father Brown, knowing Valentin's style of reasoning, leaves odd clues for
Valentin to see, assuming that Valentin will observe things that do not
obviously look like clues. Valentin's following of the `train of the unreason-
able' is not unlike Holmes's concern with `trifles'.
Understanding the differences between deduction, induction and abduc-
tion is important to social science research and to quantitative methods. It
allows researchers to understand the nature of the evidence that they are
dealing with and the nature of the inferences that are being made about
observations. Let's look a bit more closely at what is involved in the
three different types of logical thinking. Traditional deductive reasoning
is syllogistic.
For example,
All serious wounds lead to bleeding ˆ All cases of serious wounding
are cases of bleeding
This is a (case of) serious wounding
Therefore there is (this is a case of) bleeding
is an example of a valid syllogism.
38

C.S. Pierce and Umberto Eco, however, have an interest in possibilities
and probabilities, and not in strict deductive reasoning. Inductive logic
has an interest in judgements about individual cases and the build-up of
evidence.
For example,
This is a (case of) serious wounding
This is (a case of) bleeding
Therefore perhaps (it is possible that) all serious wounds lead to
bleeding
is a form of inductive reasoning.
With the statement above, you could also assert `it is probable that' as a
conclusion. This would be directly statistical, and could not be supported
by one case alone.
In Peirce's abduction, we would need to introduce a further premise
drawing or asserting a plausible connection in theory or observation, and
we would get as a conclusion not assertion of fact but a hypothesis which
would need independent testing.
Deduction in traditional logical reasoning does not involve wild guesses
or flashes of insight ± the conclusion must follow from the evidence; the
fact under consideration can be inferred from certain other facts by
means of specified general laws. The conclusion in the example of
induction on the other hand is the most plausible explanation, given the
evidence. Abductions, like inductions, are not logically self-contained, as is
the deduction, and they need to be externally validated. The conclusion
in the abduction represents a conjecture about reality which needs to be
validated through testing.
Scientists quantify their observations in deductive and inductive styles of
reasoning. Hempel gives a good example where a scientific explanation is
inductive and where statistics are applied to assist with decision-making.
When Johnny comes down with the measles, this might be explained by pointing
out that he caught the disease from his sister, who is just recovering from it. The
particular antecedent facts here invoked are that of Johnny's exposure and, let us
assume, the further fact that Johnny had not had the measles previously. But
to connect these with the event to be explained, we cannot adduce a general
law to the effect that under the specified circumstances, the measles is invariably
transmitted to the exposed person: what can be asserted is only a high probability
(in the sense of a statistical frequency) of transmission. The same type of argument
can be used also for predicting or postdicting the occurrence of a case of the
measles. (Hempel, 1965: 175)
In this example, statements about the cause of Johnny's measles take
statistical form, giving a probability of transmission. There is no `general
39

law' that says measles is ìnvariably transmitted' to the exposed person. The
relationship between cause and effect does not take universal form.
Science and social science have in common the different styles of
reasoning ± at least superficially. Deduction, induction and abduction are
quantitative. They include or exclude meanings and include or exclude
particular conclusions. Evidence àdds up'. Even guessing involves choices
that include or exclude one kind of evidence over another. But can we
simply translate notions of quantity and of measurement from science to
social science? Logic might underpin both science and social science, but
it is not clear that the phenomena of social science involve a simple
correspondence between the measure and the phenomenon.
Causality
We do not know whether 19th century social theorists such as Emile
Durkheim, August Comte or Herbert Spencer were, like Holmes, cocaine
addicts. But like Holmes they did attempt to define their research in terms
of the principles of the science of the day.
Sociological explanation consists exclusively in establishing relationships of
causality, that a phenomenon must be joined to its cause, or, on the contrary a
cause to its useful effects. (Durkheim, 1964)
The implication here is that all reasoning in social science research is
deductive and that all facts can be referred back to general laws. But, as
we have seen, there are different styles of reasoning in detective fiction and
not all our thinking or our conclusions are necessarily referable to general
laws. Detectives, social scientists and ordinary human beings are often
`meta-betters', taking punts on knowledge and predicting what is going
to happen in everyday life without full knowledge about the possible
consequences.
Durkheim, however, has a point about èstablishing relationships'.
Holmes in his analysis of Watson's thoughts is trying to establish a relation-
ship between what he sees and what he knows about Watson and what
Watson is, in fact, thinking. But Holmes cannot confirm his ideas of cause
and effect until he talks to Watson. Much of quantitative social science
research is about modelling relationships ± finding out how phenomena
are related ± before causation is established.
Textbooks often make a distinction between necessary and sufficient
causes. A necessary cause is a precondition without which a certain con-
sequence will not come about, but which does not guarantee that this
consequence will come about. A sufficient cause does guarantee the
consequence. For example, a mixture of violently inflammable gases is a
necessary cause for a gas explosion but not a sufficient one, or we would
have more of them; setting a light to such a mixture, by contrast, is a
sufficient cause. Becoming a Catholic monk is a sufficient cause for getting
40

a habit; being a man is a necessary but not sufficient cause for becoming a
monk. The distinction between `necessary' and `sufficient' causes can be
fuzzy because what is `necessary' and what is `sufficient' may sometimes
be a matter of point of view.
Trying to isolate causes is, of course, basic to detective fiction. Ellery
Queen's novels provide readers with all the clues needed to solve the
crime. It is up to the reader to try to establish the relationships between
the clues and to deduce the cause of the crime (the killer or killers). `By the
exercise of strict logic and irrefutable deductions from given data, it should
be simple for the reader to name at this point the murderer of Abigail Doorn
and Dr. Francis Jannery. I say simple advisedly. Actually it is not simple; the
deductions are natural, but they require sharp and unflagging thought'
(Queen, 1983: 199).
The quantitative social scientist, however, is often in the position where
he or she is trying to establish relationships but not trying (or not able)
to establish causation. Correlation and causation are not the same in
quantitative research methods. The reader of Ellery Queen's novels, for
example, may come up with a statement of relationships between clues
(correlation) but get the answer to the identity of the killer (causation)
completely wrong ± even though some of the reader's suggested relation-
ships between clues are, in fact, correct.
Establishing relationships and establishing causation can be different. In
defining our inquiry therefore it is worthwhile trying to `map' our thoughts
about the possible relationships between different phenomena that we
observe. Sometimes it is worthwhile doing this graphically to check the
logic of the relationships between phenomena.
Mapping Relationships
Turning a verbal statement into a diagram can be a useful first step in
defining our research. Here are two paragraphs from Pugh and Hickson
(1989: 115) with the points numbered for the diagram following:
Innovative firms have an `integrative' approach to problems. They have a will-
ingness to see problems as wholes (1) and in their solutions to move beyond
received wisdom (2), to challenge established practices. Entrepreneurial organisa-
tions [in this context just another way of saying `innovative organisations'] are
willing to operate at the edges of their competence, dealing with what they do not
yet know (2 repeated). - - -
They contrast very strongly with firms with a `segmentalist' approach. These see
problems as narrowly as possible, independently of their context. Companies like
this are likely to have segmented structures (3); a large number of compartments
strongly walled off from one another ± production department from marketing
department, corporate managers from divisional managers, management from
labour, men from women. As soon as a problem is identified it is broken up
and the parts dealt with by the appropriate departments. Little or no effort is
given to the problem as an integrated whole. ± So entrepreneurial spirit is stifled
and the solution is unlikely to be innovative.
41

All the words in these sentences create a meaningful picture of organiza-
tions ± especially the second kind. But a diagram puts it more succinctly.
Here is the diagram drawn from the numbers in the sentences:
Changing `move beyond received wisdom and operate at the edges of
competence' to the Australianism `give it a go' is a free translation. There
is no arrow-head on (3) because arrows go from cause to effect ± or
more properly from independent to dependent variables of a pair ± and
in this case the author does not tell us which causes which. Sociological
common sense suggests that it should be a double arrow or one with points
on both ends because each will maintain and enhance the other in a vicious
circle, but this is diagramming two paragraphs and they do not say this
themselves.
When we are linking variables common sense will usually tell us which
way the arrows go, but there are rules of thumb. Here is a list of rules, from
Harvard Sociology's Davis of the `Davis d' (Davis, 1985: 11±16)
1 'Run the arrow from X to Y if Y starts after X freezes.' Run an arrow from
(e.g.) childhood schooling pointing to adult income but not the other
way round, because childhood schooling is over before adult income
starts and nothing outside of science fiction can change the past.
2 `Run the arrow from X to Y if X is linked to an earlier step in a well-
known sequence'; this is merely an extension of the first rule, for when X
did not actually stop happening (`freeze') before Y started, but it still
came first in a sequence of events.
3 'Run the arrow from X to Y if X never changes and Y sometimes
changes'; thus never put sex (for example) at the pointed end of the
arrow ± sex can cause all sorts of things, but nothing in the world can
cause widespread sex-changes. Birth year, race, and national origin
work the same way.
4 'Run the arrow from X to Y if X is more stable, harder to change, or more
fertile'; a `fertile' event or quality is one well known to have a lot of
effects, like being married or not or living in this or that neighbourhood.
Davis lists some other contrasts between the `relatively sticky' and
`relatively loose' attributes, the former probable causes and the latter
probable effects. Here is part of it; note that the left and right concepts
on the one line are not juxtaposed ± it is just two lists:
Non-segmented structure
(3)
Tendency to see (1)
problems as wholes High innovativeness
Tendency to (2)
‘give it a go’
42

Relatively sticky Relatively loose
religious preference presidential popularity
occupational prestige happiness, morale
household composition stands on political issues
political party identification media habits
Intelligence Quotient preferences for candidates (or brands)
Now let's go to another and more complicated causal diagram, again start-
ing with the statement as read: This passage is from an article in Higher
Education Research Development (1984: 66) reporting a study of Australian
National University students:
Of the independent variables, age was found to be the best predictor of academic
performance in Behavioural Science students (1). [This] could be explained, first,
by their higher motivation and determination to succeed in their study as
compared to younger age students (2). As evidence of this, many researchers
(e.g. Boon, 1980) have reported these students as having few motivational prob-
lems (2 again) and as being conscientious and hard working in their approaches
towards study (3). The fact that older age students undertaking tertiary study
generally enter self-selected courses (4), and are most willing to make consider-
able personal sacrifices (5) may well explain their high motivation and determina-
tion. Secondly, older age students on the whole have the distinct advantage (6) of
accumulated knowledge and experience (6) due to maturity, referred to by Knox
(1977) as `crystallized intelligence', which would enhance their academic perform-
ance (7), and be useful particularly in the study of Behavioural Science. Thirdly, a
large proportion of older age students undertake their studies on a part-time basis
(8). The observed difference in the academic performance of these students may
be a function of their different attendance patterns. There is considerable evidence
of part-time students performing better than full-time students (9) (e.g. Butterfield
Kane, 1969).
Let us look at a possible diagram:
(2)
(4) More self- Higher motivation,
selection of determination to succeed
courses
(2)
More personal
sacrifices made Better
(5) to study performance (1)
Students (7)
older
More accumulated
(6) knowledge
(9)
More often
part-time
(8)
43

We have not run an arrow for (1) directly from òlder students' to
`better performance' because the argument purports to explain all this
in terms of the other variables. The statement (3) has no arrow because it
relates to a statement of evidence for causation rather than of causation
as such.
The arrow from `motivation/determination to succeed' to `better
performance' has no number because the argument does not actually
say that the two factors are positively linked. This is unlike (7) and
(8) where we are told and given references for the ideas that
àccumulated knowledge' and `being a part-timer' in fact goes with better
performance.
Sherlock Holmes talks in the language of `cause and effect'. It is possible,
as Umberto Eco says, to conceptually map Holmes's arguments of `causa-
tion' and to decide where Holmes is guessing and where he is not; where
the evidence for the links between cause and effect are clear and where they
are not. In social science research it is also possible to conceptually map
causal relationships, even if we have not measured these relationships. In
the diagramming above we have briefly raised the idea of relationships
between phenomena ± hypothesizing relationships and independent and
dependent variables, what Holmes might call his `trifles'. Let's now ex-
amine these trifles in more detail.
TOOLS OF MEASUREMENT
ÀM CROSSING TO GET MEXICAN DIVORCE STOP WILL MARRY CHRIS STOP GOOD
LUCK AND GOODBYE CRYSTAL' (Chandler, 1944: 18)
This is a telegram Derace Kingsley received from his wife. Kingsley knew
that his wife was having affairs but doubted the truth of the note. He
employed Phillip Marlowe, Chandler's famous seedy detective, to track
down the truth. Marlowe goes through a detailed discussion with
Kingsley to find out the context of Crystal's disappearance. Marlowe,
in this story, has ideas about the relationships between events associated
with Crystal's disappearance and, as the story unfolds, the causes of her
disappearance.
Hypotheses in detective fiction are statements about the relationships
between possible facts or observations. In the social sciences we also have
hypotheses as statements of possible facts. These statements normally go
through a process of operationalization ± procedures for classifying, order-
ing and measuring variables. In social science research there are two major
types of measurable hypotheses ± correlational and causal.
Correlational statements take the form:
Ìs there a relationship between X and Y?'
44

Correlational hypotheses test a hypothesis about two or more variables by
measuring the variables to see if they are related. The statement `People
with unstable marriages are more likely to have atheistic upbringings'
would be a correlational hypothesis. It is not a hypothesis where you
could properly manipulate a variable ± require people to have a particular
type of upbringing for the sake of a study ± or say that one variable depends
on another.
Causal statements take the form:
`If you manipulate the independent variable I, then you will observe a
change in the dependent variable D'.
Correlational hypotheses can be `causal', but the independent variable is
not (or cannot be) manipulated. Experiments are often associated with the
more traditional causal hypotheses. Experimenters try to vary the indepen-
dent variable(s) and account in a controlled way for other variables that
might be mistaken for causes. The word `make' in a sentence suggests a
causal hypothesis. `A private education makes people more tolerant of
extra-marital sexual behaviour' would be a causal statement. But could
we manipulate the independent variable? Could we ethically change a
person's potential education to see what the effects would be?
Criteria for good hypotheses are logical and not mathematical.
Hypotheses must be:
1 consistent with current knowledge;
2 logically consistent (if a hypothesis suggests that A ˆ B and B ˆ C, then
A must also be equal to C); if reading The London Times implies a
knowledge of current affairs, and a knowledge of current events
means greater participation in social activities, then readers should ex-
hibit greater participation in social activities;
3 parsimonious (the simpler the better);
4 testable and/or realistic.
One of the most difficult tasks for the social scientist is to define the con-
structs and variables within the study and the hypothesis. The definition
and measurement of variables are intimately linked.
What are Variables?
In the social sciences we assume that attributes of a phenomenon are
measurable ± male and female are, for example, attributes of `sex'. When
we say something is measurable then we are saying that attributes possess a
structure that is quantitative and therefore quantifiable. In what sense are
these attributes measurable? The most commonly used definition of meas-
urement in the social sciences is the one formulated by Stevens (1946). He
said that measurement is the assignment of numbers to objects or events
45

according to rules. We assign numbers to attributes in such a way that the
properties of the attributes are faithfully represented by the properties of
the numbers. Variables are, therefore, the embodiment of both constructs
that we want to define and the numbers that we use to represent them.
A variable is a general class of objects, events, situations, characteristics
and attributes that are of interest to the researcher. In the social sciences we
are usually interested in variables to do with people. The psychologist, for
example, is interested in behavioural or psychological variables such as
cognitive ability, personality and psychophysiological reactions, such as
stress. The main feature of a variable is that it can have different values.
Your age may be different from that of your best friend, your income may
be different from your best friend's income. The values a variable can take
on vary. Importantly, these attributes or variables are measurable.
We do not investigate variables in isolation. The basic aim of any quanti-
tative research is to investigate how variables interact with each other. Some
investigations simply look at how variables co-relate. But on other occa-
sions, we might ask more specific research questions about the nature of
these relationships. We might, for example, ask whether one variable X (say,
amount of time spent studying for an exam) influences another variable Y
(final mark on that exam). As mentioned in the brief discussion on causal
hypotheses, we refer to variable X as the independent variable and Y as the
dependent variable. The independent variable has an impact on the depen-
dent variable. In other words, the values that the dependent variable takes
on are influenced by the independent variable. The relationship may not
necessarily be causal, because the ability of the student may also influence
his or her final exam mark, not just the amount of time spent studying. Be
careful therefore of causal imagery inherent in this relationship.
Variables can be operationalized at various levels of measurement.
Stevens (1951) distinguished four levels of quantification or measure-
ment ± nominal, ordinal, interval and ratio measurement. Nominal or
categorical ± level measurement consists of unordered categories. Each
category can be given a name or a number. For example, the variable `gen-
der' has two categories or levels, male and female. We can use the words
`male' and `female' to identify people that belong to each category or we can
assign numbers to each category such that the number represents that
category. For instance, the number 1 may be assigned to represent `females'
and the number 2 to represent `males'. This level of measurement allows us
to assess whether people are from the same or a different category.
Ordinal-level measurement has the properties of nominal scales with the
additional property that the categories can be rank-ordered. If the categories
of a variable are ordered, that is, category B has `more' of the phenomenon
being measured than category A, then we say that that variable can be
measured on an ordinal scale. We assign numbers to each category such
that the ordering property inherent in the variable is preserved by the
numbers or scores assigned. For instance, if John is taller than Bill, we
can assign the number 2 to John and 1 to Bill. The number 2 is greater
46

than 1, so the relationship between these two numbers preserves the height
relationship between John and Bill. The property then allows us to rank-
order the values of variables measured on ordinal scales. These ranks can
then be validly compared.
Interval-level measurement has the defining property that equal intervals
on a scale represent equal amounts of the quantity being measured. If we
are measuring income in dollars, then the difference between annual
incomes of $45,000 and $50,000 is the same amount as the difference
between someone who earns $55,000 and someone who earns $60,000.
That is to say, there is a difference of $5,000 and that difference is `the
same' (representing the same monetary value) for each comparison of
incomes. Similarly, assume you are asked to rate the content of three tele-
vision programmes in terms of humour using a five-point scale where `0'
means `not at all funny' and `4' means `extremely funny'. If we can demon-
strate that the difference (in terms of the amount of humour represented in
the variable) in ratings between `0' and `1' is the same as the difference
between ratings of `3' and `4', then we are using an interval scale. Clearly,
establishing this property in this case may be difficult. As Watson et al.
(1993: 38) noted, `It is possible to specify, to some degree, what properties
the observations should have in order to lead to interval scale measurement
and then to investigate whether these properties are actually met by the
observations'. Cliff (1996) argues on the other hand that in the social
sciences we can only achieve ordinal-level measurement.
A fourth level of measurement, ratio-level measurement, has all the prop-
erties of ordinal and interval measurement. However, ratio measurement
has the additional property that equal ratios between numbers on the scale
represent equal ratios of the attribute being measured. Height measured in
centimetres (cm) is an example of ratio measurement. Someone who is
180 cm tall is twice the height of someone who is 90 cm tall. Similarly,
weight measured in kilograms (kg) is a ratio measure. A person who is
120 kg is twice the weight of someone who is 60 kg; someone weighing
90 kg is twice the weight of someone weighing 45 kg. An additional prop-
erty of ratio measurement is that there is a zero point on the scale that
indicates the absence of the attribute being measured. The examples of
weight measured in kilograms and height measured in centimetres both
have a zero scale (i.e. 0 kg or 0 cm) value that indicates the absence of either
weight or height.
It is difficult to establish whether many types of measures in the social
sciences are in fact interval- and ratio-level measurement. The fact that
many texts, including this one, use natural science examples to show how
interval and ratio scales work is itself an indication. Indeed many research-
ers argue that there are relatively few examples of ratio-level measurement
in the social sciences. Are there other ways of classifying or describing data
obtained from variables? Data may be referred to as qualitative when the
scale used for measuring that variable is a set of unordered categories, that
is, the level of measurement is nominal. In this case the categories are
47

qualitatively different; they do not vary in magnitude or quantity. Nominal
measures are often called discrete variables because they cannot be subdiv-
ided. Means and medians are not normally calculated for discrete variables.
When data from variables vary in magnitude, they are referred to as quan-
titative data. Variables measured on interval or ratio scales can be described
as quantitative. Interval and ratio measures are often called continuous vari-
ables because they can be subdivided. The nature of ordinal data is a little
fuzzy. Ordinal scales consist of categories, therefore they can be thought of
as qualitative. Ordinal scales also have categories that are greater than or
less than each other in magnitude and are therefore quantitative. Ordinal
scales, however, are normally treated as discrete variables (Agresti and
Findlay, 1997).
Operational Definitions
The levels of measurement represent the mathematical possibilities
available to you for quantitative analysis ± such as adding, subtracting,
multiplying and dividing ± when you have decided how you want to define
the phenomenon you want to study; how to measure your observations.
Definition, however, precedes measurement. Some phenomena are easier to
define and to measure than others. For example, sex, already mentioned,
can be measured with the values 1 representing `female' and 2 representing
`male'. But you cannot subtract `male' from `female' or divide them!
If I say that I want to operationalize `gender' as a nominal variable, I am
unlikely to encounter great debate. But not all constructs or phenomena are
that easy to measure or that easy to get an agreement on. This is not sur-
prising ± in social science most if not all phenomena that we wish to study
come from everyday life or from phenomena that are not easily observable.
We use language to describe and to define the phenomena that we wish to
measure. We try to measure constructs described by language that we hope
corresponds to the phenomenon of interest. Figure 3.1 summarizes the steps
in measurement.
Your `construct' is your idea about the phenomenon that you want to
measure. Your operational definition is your statement about how you want
to measure your construct. The construct `deliquency', for example, might
be operationally defined by `being arrested more than once prior to the age
Operational
Definitions
Variables
Construct
The Phenomenon
FIGURE 3.1 Operationalization
48

18'. In a questionnaire you might have the question (your variable) `Have
you been arrested more than once prior to the age 18? Yes. No.' This is a
nominal-level question. This is one variable. It is also possible to imagine
other definitions and operational definitions of the construct that might
be useful.
Defining and measuring our observations in social science can be affected
by the society that we live in. For example, The Information Bulletin of the
Reich Association of Aryan Christians in Nazi Germany sought to quantify
Aryanism ± the idea that blonde blue-eyed people are superior to everyone
else ± in order to reduce uncertainty among Christians about who and who
was not a Jew. The Association provided Christians with definitions of what
constituted `Aryan':
Question: A man has two Jewish grandparents, one Aryan grandmother and a
half-Aryan grandfather; the latter was born Jewish and became Christian only
later. Is this 62 percent Jewish person a Mischling or a Jew?
Answer: The man is a Jew according to the Nuremburg Laws because of the one
grandparent who was of the Jewish religion; this grandparent is assumed to have
been a full Jew and this assumption cannot be contested. So this 62 percent Jew
has three full Jewish grandparents. On the other hand, if the half-Aryan grand-
father had been Christian by birth, he would not then have been a full Jew and
would not have counted at all for this calculation; his grandson would have been a
Mischling of the First Degree. (Friedlander, 1997: 158)
Such statements are, for all intents and purposes, `operational defini-
tions'. They are quantifications. But they are quantifications based on in-
ferences about observations that are biased by society. Moreover, the
definitions themselves have social consequences. Being a Mischling meant
survival, of course. Mischling were treated better than full Jews. The con-
struct `Jew', therefore, was not a neutral category, nor was it a `natural'
phenomenon.
Let us take another example from a well-known scholar.
The Jew, who is something of a nomad, has never yet created a cultural form of his
own and as far as we can see never will, since all his instincts and talents require a
more or less civilized nation to act as a host for their development. . . . The Aryan
consciousness has a higher potential than the Jewish; that is both the advantage
and the disadvantage of a youthfulness not yet fully weaned from barbarism.
(1997: 171)
No. This is not a statement from Adolf Hitler or Joseph Goebbels. It is
Carl Jung, the famous psychoanalyst, in 1934 singing the praises of
National Socialist Nazi Germany. Can we infer from Jung's statement that
he is an anti-semite? Is Jung, at base, no different from other Nazis? Jung
belongs to the same style of reasoning about Jewishness. He uses the same
language as everyone else in Nazi Germany. He does not need the fear of the
49

Gestapo (barely formed in 1934) to come up with his ideas about Aryan
civilization.
Nazi German scientists, psychologists and psychiatrists were committed
to the idea of Aryan superiority and Jewish inferiority and tried to measure
these constructs as if they were natural phenomena. Such `measures', of
course, have little to do with science and `natural phenomena' and a lot
to do with extreme and dangerous prejudice. The example highlights
the problem with measurement in social science. Prejudice is the real
phenomenon of interest in the example from Nazi Germany. `Deductions'
about Aryanism made by Nazi Germans of good will, though, show that
styles of reasoning ± deduction, induction and abduction ± are not
necessarily `neutral' forms of reasoning. There were deductive premises
associated with `Jewishness' in the minds of Nazis. Observations were
used to reinforce those premises as if there were a universal law about
Aryanism and Jewishness. The authors have called deduction, induction
and abduction `styles of reasoning', following Ian Hacking's (1982) phrase,
precisely because those styles may be subordinated to the ideology of
the day.
Contemporary Views on Measurement
In his account of Dr Watson's thoughts Sherlock Holmes said he was being
deductive when he was, in fact, guessing. In social science we deal with
constructs and try to provide measures for these constructs. For example,
we assume that a measurement of the construct `self-esteem' is also a
measurement of the phenomenon `self-esteem'. We are, in some senses,
`meta-betting', even at this stage. As you have seen, we have to be very
careful. Does the measurement of the construct really measure the under-
lying phenomenon?
Recall that Stevens' definition of measurement involves the application of
a set of rules for assigning numbers to objects, people, attributes and so on.
In recent times, this definition of measurement has been questioned inside
and outside of statistics. Michell (1997, 1999) argues that there is a discrep-
ancy between a traditional understanding of measurement in the natural
sciences and the Stevens definition of measurement. The traditional view of
measurement is the discovery of real numerical relations (ratios) between
things (magnitudes of attributes), and not the attempt to construct conven-
tional numerical relations where they do not otherwise exist (Michell, 1999:
17). Michell illustrates this point as follows:
In measurement, according to the traditional view, numbers (or numerals) are not
assigned to anything. If, for example, I discover by measuring it that my room is 4
metres long, neither the number four nor the numeral 4 is assigned to anything,
any more than if I observe that the wall of my room is red, either the colour red or
the word red is thereby assigned to anything. In neither case am I dealing with the
assignment of one thing to another. Considering the ratios of magnitudes and
50

the numbers involved in measurement, it is clear that one is not dealing with the
relation of assignment. One is dealing, rather, with predication. That is, it is not
that my room or its length is related to the number four, the length of my
room relative to the metre simply is the number four.' (1999: 17)
Michell says that quantitative science involves two tasks, namely (1) inves-
tigating that the attribute of interest is in fact quantitative, and (2) devising
procedures to measure the magnitude of quantitative attributes. In the
social sciences, and especially psychology, researchers have assumed that
variables are quantitative. We assume, for example, that psychological vari-
ables such as self-esteem and extroversion are by their nature quantitative.
For Michell (1997), though, phenomena like self-esteem have no clear unit
of measurement compared with a cricket pitch where the measure of the
pitch is related to the pitch.
This sounds a warning to us about the nature of measurement in the
social sciences, but it is not a warning to reject measurement altogether.
Let's investigate a theorist who attempted to measure a complex phenom-
enon ± how cultures vary. Geert Hofstede applies a contemporary view of
measurement. He knows that he is measuring constructs. He is also aware
that there are issues associated with the relationship between the definitions
of a construct and its measurement.
GREAT SOCIOLOGICAL DETECTIVE STORIES: Collecting Data
Across Cultures: Can we measure cultural variation? Culture's
Consequences (Geert Hofstede)
Geert Hofstede is a sociological detective who worked on a global scale. He
raised questions about the problems associated with the creation of a world
culture before globalization, personal computers and the internet became
trendy in the study of intercultural communication. Hofstede wanted to
quantify how cultures vary and why. He conducted surveys in 66 countries
within subsidiaries of a large multinational business. He ran the pioneer
international surveys twice, in 1968 and 1972, producing a total of over
116,000 questionnaires.
The origin of Hofstede's major study was a multinational company's
concern with employee morale. HERMES, the cover name Hosftede gave
to the multinational company to protect its identity, was a service company
that had employees and customers located throughout the world. An
important part of the corporate philosophy was that customer satisfaction
and employee morale were related. Employee attitude surveys fitted well in
this context. Hofstede headed a team to prepare the first internationally
standardized questionnaire for the simultaneous survey of the corporation's
personnel.
51

Methodology and Theory
In order to study corporate morale on an international scale Hofstede devel-
oped a methodology that enabled him to measure employee attitudes in
different cultural contexts. He did not have at hand a simple methodology
to assist him. Methodology is `the science of finding out' (Babbie, 1986: 6). It
is the philosophical and theoretical underpinning of research that affects
what a researcher counts as evidence. Methods are the actual techniques,
like Hofstede's international questionnaires, and procedures used to quan-
tify and to collect data. While `methodology' and `methods' are different
conceptually they are of course related. Methodology affects method choice.
When Sherlock Holmes told Dr Watson `you know my method', he was
combining in this phrase both his assumption about law-like behaviour and
the actual techniques of deduction that he said he used. The distinction
between `nomothetic' and ìdiographic', raised briefly in Chapters 1 and
2, relates to theory and methodology. Nomothetic and idiographic represent
different styles of inquiry. Understanding society `from the inside' and
through definitions of its members has been called ethnoscience, ethnogra-
phy or ethnomethodology (among others). Understanding society `from the
outside', by the creation of general classifications or general laws of behav-
iour, has been called functionalism, positivism or empiricism (among
others). Hofstede was faced with a difficulty. An ìdiographic' approach
would assume that each culture is unique and no one law or classification
can govern them all. A `nomothetic' approach would suggest there are
comparisons that can be made across cultures and values that affect all
cultures. `The pure idiographer will probably shy away from quantitative
data and the use of statistics. Those collecting comparative data that lend
themselves to statistical analysis will be attracted to different statistical
methods according to their degree of nomotheticity' (Hoftstede, 1984: 33).
Detectives in detection fiction also have their `degree of nomotheticity'.
Some detectives try to see whether there is a typical kind of behaviour
(called ìdeal types' in sociology), and back it up with examples. This is
idiographic (and inductive, of course). Other detectives assume `law-like
theories' that enable them to predict what is going to happen. This is
nomothetic. Dr Spock in the science fiction Star Trek is presented as a
cold, calculating, character who thinks only logically and scientifically
(rather than emotionally). This is, perhaps, like Sherlock Holmes, the stereo-
type of the `nomothetic' model.
Hofstede decided to take a middle road ± combining the specific and
the general. His theory was based on the idea of `mental programmes'.
Each person, group and culture, says Hofstede, carries a certain
amount of mental programming which is stable over time. He says that
in everyday life we often use constructs to describe these mental
programmes ± for example àll members of the family will come if I ring
the dinner bell'. The task for Hoftstede therefore was to look for measures
of the constructs that describe mental programmes associated with
52

cultural values ± `to find observable phenomena from which the construct
can be inferred' (1984: 17).
Method
Hypotheses and Operationalization
Hoftstede's theoretical hypothesis is that cultural values ± specific quantifi-
able dimensions of cultural value ± have consequences for organizational
behaviour (and for human behaviour generally) and the `mental pro-
grammes' associated with this behaviour. Às nearly all our mental pro-
grams are affected by values, nearly all are affected by culture, and this is
reflected by our behaviours' (1984: 23). Hofstede defined `values' as à
broad tendency to prefer certain states of affairs over others' (1984: 18).
Cultural values are ìndependent variables' for Hofstede and a diagram
would look something like this:
Cultural values ! Structure and functioning of institutions (e.g.
education, religion)
Hofstede's literature review covered cross-cultural or cross-national studies
from the disciplines of psychology (cross-cultural psychology), sociology
(organizational psychology), anthropology, political science, economics,
geography, history, comparative law, comparative medicine and inter-
national market research.
Hoftstede identified from his literature review and preliminary analyses
(he of course pre-tested his questionnaires) what he thought were four
major dimensions of cultural value ± individualism, power distance, un-
certainty avoidance and masculinity. He created 60 core questions, 60
variables, for his questionnaire which clustered in four main areas.
1 Satisfactions ± `supply a personal evaluation of an aspect of the work
situation ± `How satisfied are you with . . . ' but also `How do you like
your job ± the kind of work you do?'
2 Perceptions ± subjective descriptions of an aspect or problem of the
work situation ± `How often does your manager expect a large amount
of work from you?'
3 Personal goals and belief ± statements not about the job or the company
as such but related to an ideal job or to general issues in industry ± for
example `How important is it to you to have an opportunity for high
earnings?'
4 Demographics ± age, sex, years of education, years with the company,
and so on.
Table 3.1 gives a brief overview of Hoftstede's process of operationalization.
53

Let's look at how Hofstede went about constructing the dimensions of
culture, the `cultural values', from his variables. Two of his major dimen-
sions, individualism and masculinity, were derived from the questions in
Table 3.2. These questions, which were prefaced with `How important is it
to you to . . . ', were designed to cover key issues such as desire for, say, a
sense of freedom (which would be related to individualism) and desire for
greater earnings (masculinity).
A man might, of course, provide answers that would be classified in the
`feminine' dimension. On the masculinity dimension, Hofstede confirmed
previous findings on gender differences ± that there are significant differ-
ences in responses from men and women:
More important for men:
Advancement
Earnings
Training
Up-to-datedness
More important for women:
Friendly atmosphere
Position security
Physical conditions
TABLE 3.1 From construct to operational definition
Construct Defined as Operationally defined by
Cultural values `a broad tendency to prefer Scores/indexes for individualism,
certain states of affairs over uncertainty avoidance, power
others' (1984:18) distance, masculinity
TABLE 3.2 Actual questions used to construct individualism/masculinity indexes
Challenge ^ Have challenging work to do ^ work from which you can get a personal sense of accomplishment
Desirable area ^ Live in an area desirable toyou and your family
Earnings ^ Have an opportunity for high earnings
Cooperation ^ Work with people who cooperate well with one another
Training ^ Have training opportunities (to improve your skills or learn new skills)
Benefits ^ Have good fringe benefits
Recognition ^ Get the recognition you deserve when you do a good job
Physical conditions ^ Have good physical working conditions (good ventilation and lighting, adequate work
space, etc)
Freedom ^ Have considerable freedom to adapt your own approach to the job
Employment security ^ Have the security that you will be able to work for your companyas long as you want to
Advancement ^ Have an opportunity for advancement to higher level jobs
Manager ^ Have a good working relationship with your manager
Use of skills ^ Fullyuse your skills and abilities on the job
Personal time ^ Have a job which leaves you sufficient time for your personal or family life
Source: (1984:155)
54

Manager
Cooperation
Hofstede's sociology is an ambitious attempt to bridge the `idiographic' ±
the individual motivations and desires of individuals in their local situation
± with the `nomothetic' ± the general causes and general classifications ±
cultural values ± that affect those individuals and those situations. The
results of Hofstede's analysis included a detailed ranking of countries by
the different dimensions of culture.
Variables
A more detailed examination of the results of Hoftstede's study provides a
better sense of what he was trying to achieve with the major dimensions of
culture.
Individualism and Masculinity
In individualistic countries (like the US, Australia, UK) people's personal
goals take priority over their allegiance to groups like the family or the
employer. Competition rather than cooperation is encouraged; personal
goals take precedence over group goals; people tend not to be emotionally
dependent on organizations and institutions; and every individual has the
right to his or her thoughts and opinions. These cultures emphasize indi-
vidual initiative and achievement and they value decision-making.
In collective societies (like Pakistan, Taiwan, Peru) people are born into
extended families or clans that support and protect them in exchange for
their loyalty. Identity is based on the social system; the individual is emo-
tionally dependent on organizations and institutions; the culture empha-
sizes belonging to organizations; organizations invade private life and the
clans to which individuals belong; and individuals trust group decisions.
According to Hofstede, for example, the Japanese value collectivism over
individualism, collaboration over competition.
Hofstede ranked countries on an individualism/collectivism scale. A
high score means the country can be classified as collective. A lower
score is associated with cultures that can be classified as individualistic.
Table 3.3 presents the rankings on individualism.
Countries were also be ranked by `masculine' and `feminine' traits.
Masculinity, for Hofstede, is the extent to which dominant values within
a society are male-oriented and are associated with such behaviours as
assertiveness, ambition, achievement, the acquisition of money, signs of
manliness, material possessions, and not caring for others. Ireland, for ex-
ample, tends to masculinity, on Hofstede's scores. Femininity stresses car-
ing and nurturing behaviour. Table 3.4 shows Hoftstede's rankings on this
dimension.
55

Power Distance
One of the most important questions used to measure power distance was:
`How frequently, in your experience, does the following problem occur:
employees being afraid to express disagreement with their managers?'
Answers were provided on a five-point scale from very frequently to
TABLE 3.3 Countries ranked by individualism scores
USA 11 India 21
Australia 12 Japan 22
Great Britain 13 Argentina 23
Canada 14 Iran 24
Netherlands 15 Brazil 25
New Zealand 16 Turkey 26
Italy 17 Greece 27
Belgium 18 Philippines 28
Denmark 19 Mexico 29
Sweden 10 Portugal 30
France 11 Yugoslavia 31
Ireland 12 Hong Kong 32
Norway 13 Chile 33
Switzerland 14 Singapore 34
Germany 15 Thailand 35
South Africa 16 Taiwan 36
Finland 17 Peru 37
Austria 18 Pakistan 38
Israel 19 Columbia 39
Spain 20 Venezuela 40
TABLE 3.4 Countries ranked by masculinity scores
Japan 11 Canada 21
Austria 12 Pakistan 22
Venezuela 13 Brazil 23
Italy 14 Singapore 24
Switzerland 15 Israel 25
Mexico 16 Turkey 26
Ireland 17 Taiwan 27
Great Britain 18 Iran 28
Germany 19 France 29
Philippines 10 Spain 30
Columbia 11 Peru 31
South Africa 12 Thailand 32
USA 13 Portugal 33
Australia 14 Chile 34
New Zealand 15 Finland 35
Greece 16 Yugoslavia 36
Hong Kong 17 Denmark 37
Argentina 18 Netherlands 38
India 19 Norway 39
Belgium 20 Sweden 40
56

very seldom. According to Hofstede, people in high power distance
countries, such as India, Singapore and Greece, believe that power and
authority are facts of life. These cultures instruct their members that people
are not equal and that everybody has a rightful place. Children seldom
interrupt the teacher and show great reverence and respect for authority.
Low power distance countries, such as Austria, Finland and Denmark, hold
that inequality in society should be minimized. People in these cultures
believe they are close to power and should have access to that power.
The rankings are presented in Table 3.5.
Uncertainty Avoidance
Two major questions were used in the measurement of uncertainty avoid-
ance, one associated with rule orientation and one associated with employ-
ment stability. The rule orientation question was `Company rules should
not be broken ± even if the employee thinks it is in the company's best
interests' with the answer on a five-point scale from strongly agree to
strongly disagree. The employment stability question was `How long do
you think you will continue working for this company?' with answers 2
years at the most, From 2 to 5 years, More than 5 years (but I probably will
leave before I retire), Until I retire.
High uncertainty avoidance cultures try to avoid uncertainty and ambi-
guity by providing stability for their members ± not tolerating deviant ideas
and behaviours and believing in absolute truths. They are also character-
ized by a higher level of anxiety and stress: people think of the uncertainty
inherent in life as a continuous hazard that must be avoided and there is a
TABLE 3.5 Countries ranked by power distance scores
Philippines 11 Pakistan 21
Mexico 12 Japan 22
Venezuela 13 Italy 23
India 14 South Africa 24
Yugoslavia 15 Argentina 25
Singapore 16 USA 26
Brazil 17 Canada 27
Hong Kong 18 Netherlands 28
France 19 Australia 29
Columbia 10 Germany 30
Turkey 11 Great Britain 31
Belgium 12 Switzerland 32
Peru 13 Finland 33
Thailand 14 Norway 34
Chile 15 Sweden 35
Portugal 16 Ireland 36
Greece 17 New Zealand 37
Iran 18 Denmark 38
Taiwan 19 Israel 39
Spain 20 Austria 40
57

strong need for written rules (e.g. Portugal, Greece, Germany). Countries
like Sweden and Denmark, however, prize initiative, and according to
Hofstede are more willing to take risks, are more flexible and think that
there should be as few rules as possible. The rankings for Sweden and
Denmark are given in Table 3.6.
Hofstede took his indices of cultural difference to be tentative, subject to
modification if additional empirical evidence came his way. Indeed, in
Appendix 3 of his book Culture's Consequences he explicitly asks readers to
send him information that might assist in his detective work: `Please tell
about examples from your own experience of differences in behaviour
among people, groups, or institutions which differ in their nationalities
but are otherwise comparable. Please mention the year and the place of
your observations and the precise nationalities involved' (1984: 289).
Hoftstede also asks readers to contact him if they had collected or discov-
ered any measurements that might correlate with his indices of individual-
ism, uncertainty avoidance, power distance or masculinity `(falsification is
as important as verification!)' (1984: 289).
Hoftstede recognized that his own prejudices and values might shape his
interpretation of the data ± `few human activities can be value free' (1984:
287). In Appendix 2 of Culture's Consequences he outlines his own values.
Hoftstede's indices, however, show that he conceives of society as a system
and that his idea of cultural values fits into the idea of a system. Social
norms, value systems of major groups of population, have a regulating
function. Social norms lead to the development and maintenance of institu-
TABLE 3.6 Countries ranked by uncertainty avoidance scores
Greece 11 Germany 21
Portugal 12 Thailand 22
Chile 13 Iran 23
Belgium 14 Finland 24
Japan 15 Switzerland 25
Yugoslavia 16 Netherlands 26
Peru 17 Australia 27
France 18 Norway 28
Spain 19 South Africa 29
Argentina 10 New Zealand 30
Turkey 11 Canada 31
Mexico 12 USA 32
Israel 13 Philippines 33
Columbia 14 India 34
Venezuela 15 Great Britain 35
Brazil 16 Ireland 36
Italy 17 Hong Kong 37
Pakistan 18 Sweden 38
Austria 19 Denmark 39
Taiwan 20 Singapore 40
58

tions (like the family) in society. It is possible to see the deductive (and
causal) reasoning in Hoftstede's conceptual schema. He is more like a
Sherlock Holmes than a Father Brown.
Hoftstede's work crosses business and academic domains. His is a good
example of a study that was constructed to address practical business con-
cerns (staff morale) and deeper theoretical issues (the nature of societies in
different countries). Hoftstede's work is also a good example of the process
of operationalization ± going from constructs to description of those con-
structs to operational definition of those constructs.
SUMMARY
Human inquiry is a social activity. Research is a way of knowing. People are
hypothesis testers even when they are not scientists. Deduction, induction,
abduction (or retroduction) are the basic processes of reasoning in science
and social science and represent different ways of testing ideas about
the world around us, natural and social. Detectives in detective fiction are
often stereotypical examples of these different styles of reasoning.
Deduction is a process of reasoning that looks on the surface to be the
most `deterministic' ± the conclusion must follow from the evidence.
Induction is where the build-up of evidence is so great that the conclusion
fits the facts. Abduction is the art of guessing, but guessing that still needs
to be tested with evidence.
The different styles of reasoning show how the logic of inclusion and
exclusion of evidence occurs. The process is, on the surface, quantitative,
because it includes and excludes options. However, the example from Nazi
Germany about attempts to quantify Aryanism shows that the styles of
logical reasoning are not necessarily a protection from the effects of ideol-
ogy and the system of beliefs within a society. The inferences from our
observations may be directly affected by our beliefs about the phenomenon
that we are studying. However, the public nature of social science ± its
openness to critique ± is intended as a protection against abuse of research.
Application of established codes of ethics is also intended as protection of
human dignity. These codes will be revisited in later chapters.
The different styles of reasoning also raise traditional theoretical concerns
about the relationship between the specific and the general; the `idio-
graphic' and the `nomothetic'. Can we really measure the big picture?
Holmes assumed that his observations of Watson's non-verbal behaviour
were referable to general laws in a process of deduction. Holmes, however,
guessed. It is easy to confuse the different styles of reasoning and to treat
phenomena as law-like when they are, in fact, not.
Many of the statements that we make in social science are statements
about relationships and statements about causation ± is one thing related
59

to another? has one thing affected another thing? The different styles of
logical reasoning deal with statements of relationships between constructs.
There is no shortage of people's statements about relationships, as we saw
in the discussion on causal diagramming. However, we also found that
mapping relationships is a complex business. We need to be careful that
the phenomena that we are investigating are logically related. Watching
television, for example, does not change you into a male or a female, but
there may be differences between males and females in their viewing
behaviour.
Statements about relationships between constructs are called hypotheses.
Social scientists often want to measure these statements and these
relationships. A statement of relationship between variables is an attempt
to measure the underlying phenomena of interest to the researcher.
Quantitative hypotheses can be correlational or causal. Correlational
hypotheses investigate relationships that may or may not be causal, but
there is no manipulation of the independent variable. Traditional causal
hypotheses assume that the researcher is going to manipulate the
independent variable. The independent variable is the assumed cause
and the dependent variable is the assumed effect.
The process of definition and measurement of variables is called opera-
tionalization. There are four major levels of measurement for variables ±
nominal, ordinal, interval and ratio. Some variables, like income, can be
operationalized at more than one level of measurement. Others, like sex,
cannot. The decision on levels of measurement is important because it will
affect the kinds of statistical analyses that are possible. For example, nom-
inal and ordinal measures ± discrete variables ± do not normally allow
calculations of mean and median, whereas interval and ratio measures ±
continuous variables ± do.
Hofstede's study is a demonstration of the language of operationaliza-
tion. The language of operationalization involves all the procedures that
lead to measurement ± from definition of constructs to definition of
variables. Hofstede's study has higher-level theoretical statements about
relationships and causes ± the `big ideas' statements ± such as the relation-
ship between `cultural values' and `institutions'. But these big ideas needed
to be defined and measured. Hofstede created a large range of variables to
study cultural values. He used more than one variable ± more than one
question in his questionnaire ± to measure each dimension. He also col-
lected demographic variables, such as age, sex, education.
Hofstede explicitly addressed the relationship between idiographic and
nomothetic approaches to analysing society and attempted to combine both
approaches in his own study. His study is `deductive', with clear ideas
about causes and effects and the law-like nature of those causes (to use
Holmes's phrase `all life is a great chain'). The extent to which
Hoftstede's general classifications ± his quantification ± of cultural values
are useful or valid is of course open to critique.
60

MAIN POINTS
. There are three major styles of reasoning in social science research.
Deduction involves conclusions about evidence that necessarily occur
after reference to certain general laws. Induction involves conclusions
about evidence after a build-up of clues. Abduction, which is like
guessing, involves conclusions that might still have to be tested with
evidence. Each of the styles of reasoning is related to social science
research because they are the basis on which we make conclusions
about evidence.
. Many of our statements are causal statements but we need to be careful
about the logical relationships between cause and effect. In social science
there are causal hypotheses and non-causal hypotheses. Correlational
hypotheses deal with statements about relationships between variables,
but there is no manipulation of variables. Causal hypotheses assume
that the independent variable is manipulated and if manipulated will
affect the dependent variable.
. Measurement assumes that the phenomenon we want to study is
quantifiable ± that it has qualities that can be measured at nominal,
ordinal, interval or ratio levels. In social science many of the phenomena
we try to measure come from everyday life. Nazi Germany's definition
of `Jewishness' and `Aryan' is an example where the phenomenon itself
is socially defined, a part of the everyday life of Germans. The measure
of the phenomenon is socially constructed.
REVIEW EXERCISES
1 Find a journal article from a sociology, psychology or media journal
that reports on a quantitative research study (this could be the same
article you used in last chapter's review exercise). Answer each of
these questions:
(a) What is the hypothesis (if there is one)? Was it causal or non-
causal?
(b) What were the major constructs in the study? How were they
defined? Were there problems with the definitions?
(c) What levels of measurement do you think were used for
operationalization of variables?
(d) What method did the author(s) say they used to collect the
data?
(e) Identify the findings (were there relationships between
variables?).
61

2 Try to put the following hypothesis into operational form:
`The more video games a child watches, the more likely they are to be
unsociable'
3 Think of at least two variables and associated levels of measure-
ment for the following constructs:
(a) boredom
(b) marital happiness
(c) deviance
(d) stress
4 For each of the following measures indicate whether they are a
measure on a categorical, ordinal, interval or ratio scale and explain
why you have chosen that level of measurement.
(a) ATM PIN number
(b) Measuring the length of cars in cms.
(c) A score on a measure of self-esteem.
REFERENCES
Agresti, A. and Findlay, B. (1997) Statistical Methods for the Social Sciences. Prentice
Hall: New Jersey.
Babbie, E. (1986) The Practice of Social Research. Belmont, CA: Wadsworth.
Chandler, R. (1944) The Lady in the Lake. Melbourne: Bolinda Press.
Cliff, N. (1996) Ordinal Methods for Behavioral Data Analysis. New Jersey: Lawrence
Erlbaum Associates.
Davis, J.A. (1985) The Logic of Causal Order. Beverly Hills: Sage.
Doubleday.
Durkheim, E. (1964) The Rules of Sociological Method. New York: Free Press.
Eco, U. (1983) `Horns, hooves, insteps', in U. Eco and T. Sebeok (eds,) The Sign of
Three: Dupin, Holmes, Pierce. Bloomington: Indiana University Press.
Friedlander, S. (1997) Nazi Germany and the Jews. London: Weidenfeld and Nicolson.
Hacking, I. (1982) `Language, truth and reason', in M. Hollis and S. Lukes (eds),
Rationality and Relativism. Oxford: Basil Blackwell.
Hempel, C.G. (1965) Scientific Explanation: essays in the philosophy of science. New
York: Free Press.
Hofstede, G. (1984) Culture's Consequences: International differencies in work-related
values. Beverley Hills, CA: Sage.
Higher Education Research Development (1984) 3(1): 66.
Michell, J. (1997) `Quantitative science and the definition of measurement in psy-
chology', British Journal of Psychology, 88: 355±83.
Michell, J. (1999) Measurement in Psychology. Cambridge: Cambridge University
Press.
62

Pierce, C.S. (1955) `Abduction and induction', in J. Buchler (ed.), Philosophical
Writings of Pierce, New York: Dover.
Pugh, D. S. and Hickson, D.J. (1989) Writers on Organizations. Harmondsworth:
Penguin.
Queen, E. (1983) The Dutch Shoe Mystery. London: Hamlyn.
Sebeok, T.A. and Umiker-Sebeok, J. (1983) `You know my method', in U. Eco and T.
Sebeok (eds), The Sign of Three: Dupin, Holmes, Pierce. Bloomington: Indiana
University Press.
Stevens, S.S. (1946) `On the theory of scales of measurement', Science, 103: 667±80.
Stevens, S.S. (1951) `Mathematics, measurement and psychophysics', in S.S. Stevens
(ed), Handbook of Experimental Psychology. New York: Wiley. pp. 1±49.
Watson, R., Pattison, P. and Finch, S. (1993) Beginning Statistics for Psychology. New
York: Prentice Hall.
63

4
Methods of Inquiry
Ìt is a capital mistake to theorize before one has data!'
Ì have no data yet. It is a capital mistake to theorize
before one has data. Insensibly one begins to twist facts to
suit theories, instead of theories to suit facts'
Sherlock Holmes,
A Scandal in Bohemia
Holmes's methods of detection, he said, were àn impersonal thing ± a thing
beyond myself'. The methods of quantitative social science research are
similarly a thing apart from us. Our research designs and our research
definitions are open to scrutiny and criticism.
Even if we guess in social science research ± abduction ± we still need to
test our guesses, our observations, with data. This is Holmes's point. `Data'
is essential before we start to make `why' or `because' conclusions from our
observations. But recognizing what is and what is not a clue, data, is itself
an art, as we saw in the last chapter. Brother Cadfael, the monk-detective in
Ellis Peters' novels, always held back on his decisions on what was and
what was not a `clue'. In The Sanctuary Sparrow a young man comes to the
abbey seeking sanctuary, safety, after being chased and beaten by men
seeking his death. The abbot asks the men why they are chasing the
young man: `My Lord, I will speak for all, I have the right. We mean no
disrespect to the abbey or your lordship, but we want that man for murder
and robbery done tonight. I accuse him! All here will bear me out. He has
struck down my father and plundered his strong-box, and we are come to
take him. So if your lordship will allow, we'll rid you of him' (Peters, 1985:
11±12). The abbey looks after the young man while Brother Cadfael inves-
tigates. `We have time, and given time, truth with out', says Cadfael (Peters,
1985: 23). Cadfael senses that the young man is innocent but does not let this
influence his thinking on innocence or guilt in his investigation.
Lord Peter Wimsey, Dorothy Sayers' aristocrat detective, is also warned
by Parker, his police friend, not to accept uncritically what appears to be
obvious. Wimsey is not amused.
`Five-foot ten,' said Lord Peter, ànd not an inch more.' He peered dubiously at the
depression in the bed-clothes, and measured it a second time with the gentleman-
scout's vademecum. Parker entered this particular in a neat pocket-book.
Ì suppose,' he said, à six-foot-two man might leave a five-foot-ten depression if
he curled himself up.'

`Have you any Scotch blood in you, Parker?' inquired his colleague, bitterly.
`Not that I know of,' replied Parker, `Why?'
`Because of all the cautious, ungenerous, deliberate and cold-blooded devils I
know,' said Lord Peter, `you are the most cautious, ungenerous, deliberate and
cold-blooded. Here am I, sweating my brains out to introduce a really sensational
incident into your dull and disreputable little police investigation, and you refuse
to show a single spark of enthusiasm.'
`Well, it's no good jumping at conclusions.'
`Jump? You don't even crawl distantly within sight of a conclusion. I believe if you
caught the cat with her head in the cream-jug, you'd say it was conceivable that
the jug was empty when she got there.'
`Well, it would be conceivable, wouldn't it?'
`Curse you,' said Lord Peter. (Sayers, 1989: 54±55)
INVOLVEMENT AND METHOD
A good research design reduces the risk of bias and of `jumping the gun' on
conclusions. A good research design is careful in its decision on what
counts as a `clue'. The men chasing the young man thought that they had
the right clues, but they did not. This is not to say that there should be no
personal involvement in research. Some methods of detection in social
science research involve the researcher as the `data collecting instrument',
such as participant observation. Participant observation ± for example liv-
ing with a traditional society in a remote village in Indonesia ± requires a
research design. Figure 4.1 provides an overview of the relationship
between methods of data collection and involvement. Social surveys and
structured interviews involve standardized questions for large groups or
populations. Semi-structured interviews and focus groups involve more
ME T H O D S O F I N Q U I R Y
Numbers
Involved
Many
Social Surveys and Structured Interviews
Semi-structured Interviews and Focus Groups
In-depth Interviews
Observation
Participant Observation
High
Personal involvement of the researcher
Few
FIGURE 4.1 Methods of data collection and personal involvement (adapted fromWorsley,1977)
65

open questions or prompts. The researcher is not personally involved with
participants. In-depth interviews, observation and participant observation,
however, assume smaller numbers and may entail greater personal involve-
ment by the researcher.
Notice that èxperiment' has not been included in Figure 4.1. Experiments
are a separate case. Small numbers of participants may be involved but
the researcher is èxperimenter' rather than `participant'. A participant
observation study, in contrast, involves the researcher directly in the lives
of the people that they are studying. The `data' or èvidence' in a participant
observation may be the accounts of the participants and the accounts of the
researcher. These àccounts' are not necessarily measured. In quantitative
studies, such as experiment, the observations are measured.
As we found in Chapter 3, the collection of statistics requires a particular
kind of research design. Figure 4.2 is a checklist on this design. We have, to
this point, introduced the whole process associated with operationalization,
including the literature review. We have not examined, however, the
methods themselves or data analysis.
Most modern research methods use a range of data collection techniques
± questionnaires, structured interviews, in-depth interviews, observation
and content analysis. The three most common forms of data collection
are case study, survey and experiment. Case studies investigate `what is
happening' and are very common in policy research and in exploratory
- exploration
- d
Type of inquiry
escription
- explanation
Units of analysis
- individuals
- groups
- organizations
Sampling
- probability
- non-probability
Hypothesis/
Research Question Time dimension
- cross-sectional
- longitudinal
Method
- case study
- survey
- experiment
Measurement
- operational definitions
Data analysis
FIGURE 4.2 Checklist for research design
66

work. A survey in comparison can cover a range of issues and normally
results in a variable by case matrix (person by age, person by education).
Questionnaire is one of the most common ways of collecting data for a
variable by case data matrix, but it is not the only way. Experiments, like
surveys, result in a variable by case matrix. In experiments, however, there
is also the intervention by an experimenter. Figure 4.3 provides a summary
of the major methods.
In the modern mind experiments are often associated with `laboratory
research', in particular experiments with rats (and white rats at that). But
the motivation for `experiments' has a long history. For Francis Bacon, a
philosopher of science, the goal of an experiment is to `put nature to the
test'. Everyone knows that science does experiments, but let us investigate
further how experiments differ from other types of methods for analysing
observations.
EXPERIMENTAL DESIGN
O, vengeance!
Why, what an ass am I! This is most brave,
That I, the son of a dear father murder'd,
Prompted to my revenge by heaven and hell,
Must, like a whore, unpack my heart with words,
And fall a-cursing like a very drab,
A scullion!
Fie upon't! foh! ± About, my brain! I have heard
That guilty creatures, sitting at a play,
Have by the very cunning of the scene
Been struck so to the soul that presently
They have proclaim'd their malefactions;
For murder, though it have no tongue, will speak
Case Study (questionnaire, interview,
content analysis, observation)
Research Question/ Survey (questionnaire, interview,
Hypothesis content analysis, observation)
Experiment (questionnaire, interview,
content analysis, observation)
FIGURE 4.3 Research methods and techniques of data collection (based on DeVaus,1990: 6.Used
by permission)
67

With most miraculous organ. I'll have these players
Play something like the murder of my father
Before mine uncle: I'll observe his looks;
I'll test him to the quick: If he but blench,
I know my course. The spirit that I have seen
May be the devil: and the devil hath power
To assume a pleasing shape; yea, and perhaps
Out of my weakness and my melancholy, ±
As he is very potent with such spirits, ±
Abuses me to damn me: I'll have grounds
More relative than this: ± the play's the thing
Wherein I'll catch the conscience of the king.
Hamlet, Act II, Scene II
Hamlet, one of Shakespeare's most famous characters, is not your tradi-
tional detective, but he took up the role of detective. Hamlet is not a scien-
tist, but he took up the role of experimenter. Hamlet was told by a ghost that
the king had killed his father. Hamlet wanted to investigate the claim.
Hamlet also wanted to create situations that tested those he thought were
participants in the murder. In this case he wanted to create a play for the
king which was a recreation of the king's murder of Hamlet's father. The
play, Hamlet thought, would get the king to declare his guilt; at least that
was the plan.
Hamlet created an experiment ± he wanted to manipulate situations in
order to observe what the effects would be. He wanted a clear and unam-
biguous sign that the king was the murderer. Hamlet found, though, that
life is messy. Trying to test everyday life has its downsides.
Columbo, the 1970's television detective, also took an experimental
approach to his detection. When he thought that he knew who the murderer
was, he would return again and again to the suspect to see what her or his
reaction would be. Each time that a suspect thought that Columbo had
finished questioning and was about to leave, Columbo would return to
ask about `. . . one more thing'. Columbo's approach was intentionally
annoying, leading the suspect to make errors.
Experiments for the scientist are the ideal way of collecting knowledge.
They allow for the identification of separate variables and keep all extra-
neous ± unwanted ± variables controlled. An experiment is `controlled obser-
vations of the effects of a manipulated independent variable on some
dependent variable' (Schwartz, 1986: 5). We might want to test, for example,
a new psychotherapy for people who have a fear of detective fiction. We
could find a sample of sufferers, have them undergo the psychotherapy and
see if their fear disappears. The problem with this approach is that even if
patients improve, we cannot be sure that the therapy was responsible. It may
be that people with a fear of detective fiction improve by themselves (spon-
taneously) or it may be that something in the therapeutic situation other than
psychotherapy itself (having someone care) was responsible for improve-
ment. The only way to find out for sure that the psychotherapy was the
68

`cause' is to control for these extraneous factors by conducting a true experi-
ment. This means creating a second group of people who fear detectives
(called the control group) but who do not get the psychotherapy. If they
improve as much as the group that does get psychotherapy, then factors
other than the psychotherapy may be the answer.
There is always the possibility, of course, that simply getting attention
from the therapist affects those with the phobia. This is a `placebo effect'. A
placebo control group, under such circumstances, might also get attention,
although not the psychotherapy, from a therapist. If both groups improved
under these conditions, then we would probably rule out the psycho-
therapy as the cause.
Figure 4.4 gives an overview of basic experimental design.
As you can see, the skill of an experiment is in the ability to control
variables, including assignment to the experimental and control groups.
Ideally, the experimental and control groups need to be the same before
the experiment starts. If the phobias of one group are greater than the other,
you can see that the results will not be reliable. Participants are often
assigned at random to experimental and control groups in the hope that
this will result in equal assignment of people to both groups.
The skill of experimental method also includes choosing a study that in
fact requires an experimental design. Examine the statements below:
1 Women believe that they are better at dancing than men.
2 Children who are sensitive to poetry in early childhood make better
progress in learning to read than those who do not.
3 Remembering a list of items is easier if the list is read four times rather
than once.
All these hypotheses involve relationships between variables. However, the
last item is most appropriate to experimental method. The first question is
about belief, rather than behaviour. The second question involves natural
Experimental Group Control Group
Measure dependent Measure dependent
variable (fear of detective fiction) The same? variable (fear of detective fiction)
Administer psychotherapy
Remeasure independent variable Remeasure independent variable
Change?
FIGURE 4.4 Basic experimental design
69

language, which, by its nature, is difficult to manipulate. The last question is
an obvious candidate for a classical experimental design.
Manipulating and controlling variables in social science research has its
limitations. Hamlet was planning to intervene in people's lives to see how
they reacted. This raises obvious issues about right and wrong ± ethics. You
cannot create brain-damaged people, for example, to see how brain damage
affects their driving behaviour. In such cases we would be looking at choos-
ing brain-damaged people after they had received the injuries from acci-
dent. Such selection is called ex post facto experimentation. The nature of the
intervention in many ways defines the experimental design that is most
appropriate for your study.
There can be little doubt that èxperimental science' has affected research
design and society itself and people's assumptions about cause and effect. If
experiments can establish causes, then identification of causes can assist all
areas of life, including business. But there is a major difference between
èstablishing cause' and èstablishing correlation'. Establishing correlation is
different from establishing causation. Kaplan (1987: 238±239) demonstrates
this in a simple way. He cites a newspaper article on stressfulness of
occupations. A study investigated 130 job categories and rated them on
stressfulness using Tennessee hospital and death records as evidence of
stress-related diseases such as heart attack and mental disorder. Jobs such
as unskilled labourer, secretary, assembly-line inspector, clinical lab
technician, office manager, foreperson were listed as `most stressful' and
jobs such as clothing sewer, garment checker, stock clerk, skilled crafts-
person, housekeeper, farm labourer, were labelled as `least stressful'. The
newspaper advised people to avoid the stressful occupations.
Kaplan (1987) points out that the evidence may not warrant the news-
paper's advice. It is possible that diseases are associated with specific occu-
pations, but this does not mean that holding the jobs causes the illnesses.
People with a tendency to heart attack, for example, might be more likely to
select jobs as unskilled labourers. The direction of causation might be that
the state of health causes job selection. Another alternative is that a third
variable is having an effect. Income levels, for instance, might affect both
stress and illness. Ìt is well known that poor people have lower health
status than wealthy people' (1987: 239).
Let's look at three possible cases of causation:
In the first, the job causes the illness. In the second, there is a tendency of
people with illnesses to select particular jobs. In the third, economic status, a
third variable, affected job choice and illness. To establish causation we
Job Illness Job
Illness Economic Status
Job Illness
70

would need to know that both X and Y variables co-vary, that X precedes Y
in time, and that no other variable is the cause of the change.
At the beginning of the 20th century the idea that experimental social
science could easily establish causes was particularly appealing to indus-
tries involved in human persuasion. The advertising industry trade journals
at the beginning of the century, for example, made it clear that an under-
standing of the psychology of audiences was essential for advertising suc-
cess and that this was what their clients were paying for. In 1920, Professor
Elton Mayo, chair of Psychology and Ethics at Queensland University, gave
the major address at the Second Advertising Men's Conference:
The ad. expert is an educator in the broadest and highest sense of the term. His
task is the persuasion of the people to be civilized. . . . You must think for the
housewife and if you do that for her and if she finds you are doing it, you will
have her confidence. . . . It is necessary to understand the fear complexes that are
disturbing our social serenity. It is not the slightest use meeting Satanism or
Bolshevism by organized rage or hate. Your only chance of dealing with these
things is by research, by discovering first and foremost of the cause of this mental
condition. (cited in Braverman, 1974: 144±5)
Mayo went on to be internationally famous in the area of industrial psy-
chology and was involved in the famous Hawthorne Experiments in the
1930s and 1940s. The linkage of scientific experimental psychological
research to commercial needs was well established in the United States
by 1920 with the publication of Walter Dill Scott's Psychology and
Advertising. In 1922, J.B. Watson, the famous behavioural psychologist,
was appointed vice-president of advertising company J. Walter Thompson.
Professor Tasman Lovell was Australia's first chair of psychology in 1923
and joined in the chorus of voices for detailed scientific research of con-
sumer attitudes. An advocate of behavioural psychology, he proclaimed the
need for advertising men to `become versed in the study of instinctive
urges, of native tendencies for the need to assert himself, ``to keep his
end up'', which is an aspect of the social instinct that causes him to pur-
chase beyond what is required'. It was not until the mid-1930s, however,
when audited circulations of newspapers were available, that advertising
firms introduced market analysis on a large scale.
J. Walter Thompson (JWT), an established American advertising agency,
employed two psychologists, A.H. Martin and Rudolph Simmat, to oversee
advertising research. Martin used mental tests he had developed at
Columbia University to measure consumer attitudes towards advertising.
In 1927 he established the Australian Institute of Industrial Psychology in
Sydney with the support of the University of Sydney's psychology depart-
ment and the Chamber of Manufacturers. The Institute brought `local busi-
ness men in contact with advanced business practices'.
Simmat was appointed research manager for JWT when it established its
Australian branch in 1929. JWT standardized art production and research
71

procedures, including segmentation of audiences. The agency divided
Australian society into four market segments, based on income. Classes
A and B were high income housewives. Classes C and D were average or
below average income housewives. Class D had `barely sufficient or even
insufficient income to provide itself with the necessities of life. Normally
Class D is not greatly important except to the manufacturer of low price,
necessary commodities' (Simmat, 1933: 12).
Interviewing techniques were also standardized by Simmat, who had
found that experience had shown that women were usually more effective
as fieldworkers than men. Èxperiments have indicated that persons with a
very high grade of intelligence are unsatisfactory for interviewing house-
wives . . . usually a higher grade of intelligence is required to interview the
higher class of housewife than is required to interview the lower grade
housewife' (Simmat, 1933: 13).
By 1932 JWT had interviewed 32,000 Australian housewives. Advertising
was targeted to specific audiences, with sophistication `definitely soft-
pedaled' for Classes C and D. `We believe that farce will be more popular
with our Rinso [detergent] market than too much subtlety.'
Lever, a soap manufacturer, was one of the first and major supporters of
`scientific advertising'. Simmat expressed Lever's vision when he said that
Àdvertising enables the soap manufacturer to regard as his legitimate
market every country where people wash or ought to wash'. Lever was
the largest advertiser of the period. In 1933±4 Lever bought 183,000 inches
of advertising space in metropolitan dailies. Soap, a simple product, crossed
all market segments.
The confidence among social scientists at the beginning of the
20th century that they could establish `cause and effect' was brazen, to
say the least. Psychoanalysts also sold their expertise in establishing
`causes' of behaviour. Take, for example, the illustrious Dr Ernest Dichter
of the Institute of Motivational Research, who in the 1950s lectured to
packed halls of advertisers
and their agents about why people buy their goods. They must have been among
the strangest gatherings held for Sydney and Melbourne businessmen.
Developing his theme that `the poorest way to convince is to give facts,' he led
his listeners into psycho-analysis, folklore, mythology, and anthropology.
He told them of some of his case histories. There was the Case of the Nylon Bed
Sheets. Women would not buy Dupont's nylon non-iron bed sheets, though they
were good quality and competitively priced. In despair they consulted Dr. Dichter.
He drew up his questionnaire and sent his researchers to interview the women.
After exploring their answers and looking into the sexual and folk associations
of bed sheets he discovered that the women were unconsciously jealous of the
beautiful blonde lying on the sheets in the advertisements. (Actually, they said
their husbands wouldn't like them.) When Grandma was substituted for the
blonde, up went the sales. (Ì'm surprised,' he said, `that most of my theories
work.') Then there was the Blood and Virility Case. Men had stopped giving
blood to the Blood Bank. When consulted, Dr. Dichter discovered they uncon-
72

sciously feared castration or loss of masculinity. The Bank's name was changed to
the Blood Lending Bank, advertisements of beautiful girls trailing masculine
blood-donors were prepared, and all went well. (Jones, 1956: 23)
Meanwhile, actual experiments were far more conservative in their conclu-
sions and far more useful than Dichter's theories (guesses?) about the
effects of advertising. Carl Hovland's experimental research on the effects
of propaganda is a good example. He provided wartime research for the
Information and Education division of the US army. Early in 1945 the Army
reported that morale was being negatively affected by over-optimism about
an early end to the war. The Army issued a directive to the troops informing
them of the difficult tasks still ahead. The Army wanted to emphasize that
the war could take longer than presumed.
The directive provided an ideal topic for research ± which messages are
best for influencing people? Hovland et al. (1971) used the directive in an
experiment on the effect of presenting `one side' versus `both sides' in
changing opinions on a controversial subject, namely the time it would
take to end the war.
The Armed Forces Radio Services, using official releases, constructed two
programmes in the form of a commentator's analysis of the Pacific war. The
commentator's conclusion was that it would take at least two years to finish
the war in the Pacific after Victory in Europe.
`One Side'. The major topics included in the program which presented only the
arguments indicating that the war would be long (hereafter labeled Program A)
were: distance problems and other logistical difficulties in the Pacific; the
resources and stock piles in the Japanese empire; the size and quality of the
main bulk of the Japanese army that we had not yet met in battle; and the deter-
mination of the Japanese people. This program ran for about fifteen minutes.
`Both Sides'. The other program (Program B) ran for about nineteen minutes
and presented all of these same difficulties in exactly the same way. The additional
four minutes in this later program were devoted to considering arguments for the
other side of the picture ± U.S. advantages and Japanese weaknesses such as: our
naval victories and superiority; our previous progress despite a two-front war; our
ability to concentrate all our forces on Japan after V-E Day; Japan's shipping
losses; Japan's manufacturing inferiority; and the future damage to be expected
from our expanding air war. These additional points were woven into the context
of the rest of the program, each point being discussed where it was relevant.
(1971: 469)
Hovland conducted an initial survey of the troops in the experiment to get
an idea of their opinions about the Pacific before hearing the broadcast in
order to compare their opinions after the broadcast. The following tables,
from Hovland's data, show that the effects were different for the two ways
of presenting the messages depending on the initial stand of the listener.
Table 4.1 shows that two-sided messages were effective for those who
already estimated a short war and one-sided messages were more effective
73

for those who estimated a long war. Table 4.2 shows that two-sided mes-
sages are more effective with high school graduates than with nongradu-
ates.
Hovland's research showed that mass-media messages can be used to
reinforce and to change attitudes. One-sided messages are most appropriate
when people already support a point of view. Two-sided, or balanced,
messages are most appropriate when people are better educated and/or
opposed to a point of view.
Different Types of Experimental Design
Hovland's study is a classical experiment ± an impact study where the
participants of the study are directly affected by the independent variables.
Estimates of when the war ended were of direct interest to the soldiers
concerned.
Not all experiments, however, are of this kind. Many studies involve
participants in processes of recognition, recall or evaluation of materials
given to them. Such studies have little direct impact on the participants.
Impact studies are the ideal, but as Aronson and Merrille Carlsmith (1968:
73±74) point out, `ethics and good taste confine us to weak empirical opera-
tions'.
The basic experimental designs are between-subject (independent) and
within-subject (related) design. If two or more totally separate groups of
people each receive different levels of the independent variable, then this
constitutes a between-subject design. If the same group of people receive all
the various levels of the independent variable, then this is an instance of
within-subject design. In the television series The Good Life, Tom is in the
TABLE 4.1 Effectivenessof ProgramAandProgramB formenwithinitiallyunfavourableandmenwith
initially favourable attitudes
Among men whose initial estimate was`Unfavourable' (estimated a short war) %
Program A (one side only) 36
Program B (both sides) 48
Among men whose initial estimate was`Favourable' (estimated a long war)
TABLE 4.2 Effectiveness of Program A and Program B for men of different educational backgrounds
Among men who did not graduate from high school (changing to a longer estimate) %
Among men who graduated from high school (changing to a longer estimate)
74

kitchen with three seed boxes. He tells his wife that he is conducting an
experiment into the effects of talking to plants. All the boxes contain the
same seeds. Box A, says Tom, will be talked to for 10 minutes each morning
in a gentle voice. Box B will be shouted at. Box C will not be spoken to.
Tom's experiment is a traditional `between-subject' design (Davis, 1995: 52).
Tom's experiment is a laboratory experiment. Experiments conducted in
the natural setting are called field experiments. Bystander apathy, for ex-
ample, has been an ongoing topic of interest to sociologists. People will
often walk past people being robbed or murdered on city streets.
Studying such a phenomenon in a laboratory is difficult. Takooshian and
Bodinger (1979) organized a national study with volunteers disguised as
street roughs. The volunteers staged mock break-ins into cars in busy city
streets. In each case, the `suspect' used a wire coat hanger to force open a car
door and then `stole' TV sets, cameras or other valuable items. The experi-
menters watched from a hideout not far away. The results for New York
showed that in only six out of 214 separate break-ins did passers-by chal-
lenge the `robbers' and then with only very mild queries such as `Does this
car belong to you?' Over 3,000 people walked past the cars. The results from
14 North American cities showed that the intervention rate varied from 0 in
Baltimore to 25 per cent in Phoenix, with an average intervention rate of
about 10 per cent.
Experiments are attempts to measure observations directly and to ensure
that confounding and extraneous variables are removed. They are direct
interventions into people's lives to see how they will react. Direct observa-
tions of, and interventions into, large populations are difficult if not imposs-
ible in social science research. Survey is one of the most common methods
for studying large populations.
SURVEY DESIGN
The time to use surveys is when you cannot observe directly what you want
to study. Roman emperors called a census to count the populations under
their control because they could not personally observe everyone and
wanted to know whom to tax (among other things). These censuses, or
surveys, were large but were not designed to answer complex questions
about the motivations of the population (for example, `do you like Emperor
Tiberius?').
The Bills of Mortality created in Britain in 1594 to survey deaths from
plague and other sicknesses are the first modern health statistics. The opera-
tional definitions of types of death included: `Appoplex and suddenly',
`Bedrid', `Blasted', `Bloody Flux, Scowring' and `Flux', `Drowned',
`Executed', `Frighted', `Griping in the Guts', `Kings Evill', `Lethargy',
`Spotted Fever and Purples', `Teeth and Worm', among others. These stat-
istics were, interestingly, concerned not only with recording deaths and
baptisms but also with the relationship between the nature of those deaths
75

and God's intentions. Was a drop in baptisms related to punishment by
God? Nurses like Florence Nightingale saw the task of quantification as an
essentially religious one. She wrote that `the true foundation of theology is
to ascertain the character of God. It is by the aid of statistics that law in the
social sphere can be ascertained and codified, and certain aspects of the
character of God thereby revealed. The study of statistics is thus a religious
service' (cited in David, 1962: 103).
Modern countries conduct regular censuses to count the population.
However, when researchers try to elicit complex information through
large-scale surveys there is no guarantee that people will provide the in-
formation the researcher wants. Karl Marx, the communist writer of the
nineteenth century, sent over 20,000 questionnaires to workers to ask
them questions about their relationships with their bosses (Marx cited in
Bottomore and Rubel, 1956). As far as we know he received no replies.
What is a Survey?
In Chapter 3 we gained an insight into the size and complexity of Geert
Hofstede's global survey of employees in a multinational company. A sur-
vey is a method of collecting data from people about who they are (educa-
tion, finances, etc.), how they think (motivations, beliefs, etc.) and what they
do (behaviour). Surveys usually take the form of a questionnaire that a
person fills out alone or by interview schedule in person or by telephone.
The result of the survey is a variable by case data matrix.
There is, of course, massive ongoing collection of data about individuals
in modern society ± via the internet and other transactions, electronic and
otherwise. These data are often used to construct a `digital persona' ± an
electronic copy of a person's behaviour and preferences for marketing and
other purposes. This is also a form of `surveying', but, as discussed in
Chapter 5, masses of data do not necessarily guarantee meaningful results.
There are three major reasons for conducting surveys in modern societies
(Fink and Kosecoff, 1985: 14):
1 Planning a policy or a programme. This can be at a small-scale level
where parents might be surveyed about opening hours for a day care
centre or employees in a transnational corporation asked how they feel
about their boss.
2 Evaluating the effectiveness of programmes to change people's know-
ledge, attitudes, health, or welfare. This could include, for example,
major media campaigns, such as quit smoking. Such campaigns,
which can cost millions of dollars, require evaluation of their effec-
tiveness.
3 Assisting research and planning generally. This can include everything
from a sociologist's concern with measuring social inequality to the
census.
76

Designing questions in a questionnaire requires skill in understanding
levels of measurement (and the statistical purposes for which the questions
are going to be put); using simple language (and pre-testing that language);
and administration.
The Variable in Question
The questions in your questionnaire are your variables. Your operational
definitions ± your choices on how to measure your constructs ± should be
reflected in the variables in your questionnaire. If you have the hypothesis
`men are more likely than women to watch television', then these two
variables will be present in the questionnaire. A survey, of course, might
be based on a research question ± a general statement about an area of
interest, rather than a specific hypothesis(es). In either case you will be
dealing with variables.
The questions in a questionnaire will reflect the appropriate levels of
measurement necessary for further statistical analysis. These levels of
measurement ± nominal, ordinal, interval and ratio ± were discussed in
Chapter 3. The levels of measurement also reflect the nature of the
phenomenon you are studying. There are limits on what numbers can do
with phenomena.
Nominal Variables/Questions
Nominal-level questions are those designed to elicit responses that take
categorical form. For example, if you respond `male' to the question `Are
you male or female?', then you have provided a response to a nominal
rating scale. There is no meaningful `distance' between the numbers `1' to
represent `male' and `2' to represent `female', except that the categories are
different. It is possible to add up each of the categories and get frequencies,
but there is no such thing as `average gender' and you cannot subtract one
male from one female or multiply or divide one male and one female.
Notice also that you can never say there is nothing of the phenomenon.
You are always either male or female. The questions below are examples of
nominal-level measurements.
What type of dwelling is this residence?
1 Separate house, semi-detached,
row/terrace, townhouse, etc.
One storey ( )
Two or more storeys ( )
2 Unit/Flat
In a one or two storey block ( )
In a three or more storey block ( )
3 Other (Please specify).....................................................
77

Is any adult currently studying?
Yes ( )
No ( )
Note that question 3 is open-ended while the other questions are closed-
ended. Closed-ended questions provide only fixed choices for the respon-
dents. However, question 3 can be post-coded because each of the answers
could be classified and coded as nominal data.
Ordinal Variables/Questions
Ordinal-level questions require people to answer in rank order. Ordinal
questions have a `more or less' aspect to them. Many social science con-
structs are measured at the ordinal or rank level. A `rank' does not tell you
how far apart intervals are. For example, if you hear that the horse race ends
with first, second and third, you have a rank but you do not know the
distance between the horses. The question below is an example of ranking.
Please rank the following four items according their importance to
you in your use of the telephone. The top ranked should be assigned
the number 1 and the lowest rank the number 4.
Business calls ( )
Talking to friends ( )
Talking to relatives ( )
Information services ( )
Interval Variables/Questions
Intelligence Quotient (IQ) is often given as an example of an interval-level
measure. There is always something of the phenomenon and the distances
between the intervals are supposed to be known. With interval level the
numbers attached to a variable imply not only that, for example, 3 is more
than 2 and 2 is more than 1 but also that the size of the interval between 3
and 2 is the same as the interval between 2 and 1. A question that asked
people whether they strongly agreed, disagreed, strongly disagreed is often
treated as an interval-level measurement in modern research even though it
looks òrdinal'. This is where it can get tricky because the issue for the
researcher is whether the distance between the interval ± the distance
between àgree' and `disagree', for example ± is meaningful. One person's
àgree' might be another person's `disagree'.
The question below, `what is your household's annual income?', would
be described by Fink and Cosecoff (1985) as an interval-level question.
Using such data to make conclusions about other constructs, however,
needs care. If, for example, we tried to measure social status using income,
then `ranges' can be deceptive. A person with a salary of $20,000 would be
in a very different `status' compared with a person on `$50,000', but the
$30,000 difference means less as we go up the scale. A person on $130,000,
78

for instance, is unlikely to be in a significantly different status group com-
pared with a person on $150,000.
What is your household's annual income?
Less than $3,000 ( ) $50,001±$60,000 ( )
$3,001±$5,000 ( ) $60,001±$70,000 ( )
$5,001±$8,000 ( ) $70,001±$80,000 ( )
$8,001±$12,000 ( ) $80,001±$90,000 ( )
$12,001±$16,000 ( ) $90,001±$100,000 ( )
$16,001±$20,000 ( ) $100,001±$120,000 ( )
$20,001±$25,000 ( ) More than $120,000 ( )
$25,001±$30,000 ( ) Prefer not to say ( )
$30,001±$35,000 ( ) Not applicable ( )
$35,001±$40,000 ( )
$40,001±$50,000 ( )
Ratio Variables/Questions
Ratio-level measures, as discussed in the previous chapter, have a true zero
point. The question below is a ratio-level question. With this ratio-level
question it is possible to say which households have twice the number of
radios compared with other households, something that you cannot do with
lower levels of measurement.
How many radios are there in this dwelling? (. . . . . . . . . . . . )
Understanding levels of measurement is partly an understanding of the
phenomenon you are studying. Sex, as a variable, for example, cannot be
operationalized as a ratio-level question. A `zero' is meaningless in this
context. Income, however, can be operationalized at all levels of measure-
ment. You can ask the question `Do you have an income?' with the reply
`Yes' or `No'. You have operationalized income at the nominal level. You
lose a lot of information, though, in such a question.
Multiple-Item Scales
Multiple-item scales have been developed to provide a more sophisticated
way of measuring people's underlying attitudes. There are three major
types of scale ± differential scales, cumulative scales and summative scales.
Each scale entails different assumptions about the relationship between the
responses an individual provides and the measurement of the underlying
attitude.
Differential Scales
Thurstone (1929) created differential scales. People are assumed to agree
with only those items whose position is close to their own. Statements
related to the attitude are gathered and submitted to `judges' who classify
79

the items according to their position on a dimension. Table 4.3 shows
Thurstone's study of attitudes towards the Church. Items on which judges
fail to agree are rejected. Items representing a wide range of scale values
form the scale and are then presented to respondents. Thurstone's items
have a definite position on the scale.
Cumulative Scales
Cumulative scales allow agreement and disagreement for each item. The
Bogardus Social Distance scale (Bogardus, 1925) was one of the earliest
scales of this type. Table 4.4 shows how the cumulative scale works. A
person who circles number 3 in respect to some group, indicating willing-
ness to have them in the street as a neighbour, would also be willing, one
would think, to allow them as citizens of the country. The scale score is
defined as the total number of items agreed with.
Summative Scales
Summative scales allow agreement and disagreement on individual items.
Respondents normally respond to an item with: (1) strongly disagree; (2)
disagree; (3) agree; (4) strongly agree. The scale score is obtained by sum-
ming the responses to each item (taking into account sign reversal for nega-
tive items). Likert (1932) scales are the most common form of summative
scale.
Table 4.5 is taken from the Mach IV scale of Christie and Geis (1970).
Mach IV is a measure of Machiavellianism and the desire to manipulate
others. The positive items ‡†, which might run Strongly Agree (4),
TABLE 4.3 Examples fromThurstone's differential scale
Scale value Item
1.2 I believe the church is a powerful agency for promoting both individual and social righteousness
3.3 I enjoy my church because there is a spirit of friendliness there
4.5 I believe in what the church teaches but with mental reservations
9.2 I think the church seeks to impose a lot of worn-out dogmas and medieval superstitions
11.0 I think the church is a parasite on society
TABLE 4.4 Examples from Bogardus Social Distance scale
To close To my To To As Would
kinship club as To my employment citizenship visitors only exclude
by personal street as in my in my to my from my
marriage chum neighbour occupation country country country
English 1 2 3 4 5 6 7
Black 1 2 3 4 5 6 7
French 1 2 3 4 5 6 7
Chinese 1 2 3 4 5 6 7
Russian 1 2 3 4 5 6 7
80

Agree (3), Disagree (2), Strongly Disagree (1), are balance by negative items
reversing the scores, Strongly Agree (1), Agree (2), Disagree (3), Strongly (4).
Each of the items relates to the construct of interest ± manipulation. Only
three of the Mach IV items are presented in Table 4.5.
Item scales are subject to special kinds of bias or error. Halo bias refers to
the tendency for overall positive or negative evaluations of the person (or
thing) being rated. Generosity error refers to raters' overestimation of desir-
able qualities of people that the rater likes. Contrast error refers to how
some raters seem to avoid extreme response categories (such as strongly
disagree). There are tests that have been created to check the validity and
reliability of items in scales and these should be used in the pilot phase.
The Words in the Question
Inspector Clouseau, the comic-clumsy French detective played by Peter
Sellers, often gets into trouble with pronunciation. He pronounces `mon-
keys' `minkeys', `phones' `ferns' and `room' `rhum'. People do not under-
stand what he is saying, until he clarifies what he has said. Questionnaires
have the same problem. You think that the sentence you have written will
be understood, but it isn't.
The same question worded in two different ways can produce different
results. Howard Schuman and Stanley Presser of the Survey Research
Center at the University of Michigan replicated in 1974 a 1940 experiment
with the following outcomes:
`Do you think the United States should forbid public speeches against demo-
cracy?' Forbid: 28% Not forbid: 72%
`Do you think the United States should allow public speeches against democracy?'
Not allow: 44% Allow: 56% (Schuman and Presser, 1977)
The words we use in a sentence can have a dramatic effect on the result. In
this case, the word `forbid' raised concerns among a large proportion of the
respondents to the survey. People may also not understand the meanings of
the words. Cannell and Kahn (1968) cited 1960s estimates that the average
American knew fewer than 10 per cent of the words in the English
TABLE 4.5 Selected examples from Christie and Geis's Likert scale
Item Strongly Agree Agree Disagree Strongly Disagree
The best way to handle people is to
tell them what they want ‡†
It is wise to flatter important people ‡†
When you ask someone to do something
for you, it is best to give the real reasons
for wanting it rather than the reasons
which might carry more weight †
81

language. Wording for questions in a questionnaire is not only a matter of
coming up with good questions that relate to the research question or
hypothesis of interest but coming up with good questions that can be
understood. An important part of questionnaire design includes under-
standing of the frame of reference of the people you are studying. Frame
of reference ± everyday life ± involves understanding the ambiguity of
language and the fact that each individual necessarily interprets spoken
or written communication from his or her own experience and personal
viewpoint.
There are three ways of dealing with frame of reference: ignore it, ascer-
tain it, or control it.
Bancroft and Welch (1946: 540±549) provide a classic illustration of the
effect of frame of reference on responses to questionnaires. They found that
the series of questions used by the Bureau of Census in the US to ascertain
the number of people in the labour market consistently underestimated the
number of employed persons. When asked the question: `Did you do any
work for pay or profit last week?' respondents reported in terms of what
they considered their major activity, in spite of the explicit defining phrase
`for pay or profit'. Young people going to school considered themselves to
be students even if they were also employed on a part-time basis. Women
who cooked, cleaned house, and raised children spoke of themselves as
housewives, even if they also did some work for pay outside the home.
The answer to this problem was to ascertain the frame of reference and to
control it. People were asked first what their major activity was; those who
gave nonworker responses were asked whether, in addition to their major
activity, they did any work for pay. This provided a simple but effective
solution.
Once the frame of reference is understood it is important to write ques-
tions that avoid any additional bias. DeVaus (1985: 83) provides a simple
checklist for the wording of questions:
1 Is the language simple? Do not use jargon or technical terms that
people will not understand. A question such as `Is your household a
patriarchy?' will be understood by some people and not others.
2 Can the question be shortened?
3 Is the question double-barrelled? Double-barrelled questions are those
which ask more than one question in the same sentence. `How often do
you visit your parents?' should be broken into a question about the
mother and a question about the father.
4 Is the question leading? Questions that make people feel that they have
to answer in a particular way are `leading'. `Do you support the
defence of our country?' is loaded. A person would feel obliged to
say `yes'. A question starting `Do you agree that . . . ` also gives respon-
dents a feeling that they are giving a wrong answer if they say `no'.
5 Is the question negative? Using `not' in a sentence can be misleading.
The question `Marijuana should not be decriminalized' ± agree/dis-
82

agree should be written `Marijuana use should remain illegal' ± agree/
disagree.
6 Does the respondent have the necessary knowledge? A question that
asks `Do you agree with the government's handling of the waterfront
crisis?' requires knowledge about the crisis. A `filter' question is used
to check whether respondents have the knowledge. `Do you know
about the current waterfront crisis?'
7 Will the words have the same meaning for everyone? If words have
different meanings for different subcultural groups, then avoid them.
8 Is there prestige bias in the question? People sometimes distort answers
to impress the interviewer. They might exaggerate income, education
or minimize their age. There is no simple solution to this. It is called a
social desirability response set. These `sets' can sometimes be identified
in analysis. However, avoiding leading questions will reduce this type
of bias.
9 Is the question ambiguous? The longer the sentence and the more
complex the wording in a question, the greater the possibility of bias.
10 Direct and indirect questions. Some topics are extremely sensitive
and, in fact, may not be allowed by an ethics committee. `Have you
had an affair that your partner does not know about?' is not only direct,
it is biased in other ways (e.g. the possibility of prestige bias). If a
question cannot be asked directly, then indirect questions need to be
created.
11 Is the frame of reference for the question clear? The question `what is
your occupation?', as an open-ended question, is reasonable, but may
receive the reply `engineer'. There are many types of engineer.
Providing categories of occupation (e.g. as defined by the census)
would assist here. Asking the question `How often do you visit your
father?' is also reasonable, but more specific information on frequency
is required.
12 Does the question artificially create opinions? You should, where
appropriate, give people the option of `don't know' or `prefer not
to say'.
13 Is personal or impersonal wording preferable? You can ask people how
they feel about something, or how they think other people feel about
something. The choice of `personal' or `impersonal' approaches to
wording will depend on the researcher's interests.
14 Is the question wording unnecessarily detailed or objectionable?
Questions about precise age, for example, might cause problems.
This is often solved by putting age into ranges.
Basic demographic questions have often been tested and re-tested by major
government census and statistics agencies in their own survey work. These
agencies publish guides to questionnaire design and the operational defini-
tions used in their own questions.
83

Administering the Questionnaire
Administration of the questionnaire involves layout, decisions on length of
questionnaire, types of questions to be asked, implementing the survey,
monitoring the quality of answers, response rates and ethics issues. Poor
administration of a questionnaire can lead to low response rates, poor qual-
ity responses and poor data generally. The questionnaire is also an `ambas-
sador' for the research project. If respondents feel that you have not taken
care in its design, then it is unlikely that they will be motivated to fill it out.
Layout
The layout of a questionnaire includes:
1 General introduction (the purpose of the questionnaire, how people
were selected, assurance of confidentiality and how and where to return
a mailed questionnaire).
2 Question instructions (how questions are to be answered).
3 Order (simple questions should go first, complex questions last; concrete
questions first, abstract questions last).
4 Creating a numerical code (a scale or other system of numbers into
which the recorded responses are to be translated).
A general introduction tells respondents about the study, but it might also
be supplemented by a letter requiring signed informed consent. In most
cases, return of a questionnaire counts as `informed consent'. However,
many studies seek signed informed consent. Appendix I is an example of
a proforma letter for informed consent, produced by Murdoch University
ethics committee. Informed consent can include agreement to publication of
data.
Well-formatted questions assist response rate and accuracy of answers.
There is a variety of answer formats. Whichever format you choose you
should be (a) consistent in use of that format and (b) consistent in the type
of response required for that format (for example, don't combine ticking,
circling, crossing out within the same format). Figure 4.5 is an example of
some commonly used formats. Contingency questions are an often-used
format. Figure 4.6 is an example of a contingency question. Contingency
questions have obvious benefits in reducing confusion.
Contingency and `go to' questions enable efficient use of space.
[ ] Agree Agree ( ) Agree
[ ] Disagree Disagree ( ) Disagree
[ ] Undecided Undecided ( ) Undecided
FIGURE 4.5 Different answering formats
84

Well-formatted questions improve the probability of getting accurate
responses. A coding book for a questionnaire involves assigning numbers
to the responses for efficient recording of appropriate and inappropriate
responses and non-responses. After people have answered questions, the
researcher needs a system for transferring those data from the questionnaire
itself to the computer. This is the role of a coding column.
Table 4.6 provides a sample coding column. The first numbers in the
`official use only' column, will identify the questionnaire (not the respond-
ent). The other numbers in the column identify the responses to each ques-
tion.
You will need to decide on a coding system for each question. This coding
system will assist entry of the data into the computer. Your `code' for the
first question, for example, has five possibilities. Your code of 1 to 5 would
cover an answer in any of the five options to question 1. There are other
possible outcomes, however, including non-responses and inappropriate
responses. A code for non-response may be 9 and a code for an inappropri-
ate response may be 0. `1' in your computer would represent the response to
`one storey separate house, semi-detached, row/terrace, townhouse, etc.',
`2', `two or more storey separate house, semi-detached, row/terrace, town-
house, etc.', and so on.
Length of Questionnaire
There are no set rules for the length of a mailed self-administered ques-
tionnaire or the length of an interview. Dillman (1978) found that the op-
timal length for questionnaires to the general public was about 12 pages or
125 items. Response rates drop rapidly if a questionnaire is longer. Surveys
for special groups, however, may be longer. A survey of social workers
about their profession, for example, is of special interest to the survey work-
ers. Babbie (1986: 22) says that a 50 per cent response rate for a question-
naire is adequate, 60 per cent is good and 70 per cent very good. Response
Were you born in Britain?
1. ( ) Yes (go to Q2)
( ) No
(a) Where were you born?____________________
(b) How many years have you lived here?______
Go to Question 2
FIGURE 4.6 Contingency questions
85

rates for mailed questionnaires increase, however, if there is a follow-up
with respondents who have not returned their questionnaire. Response
rates for telephone and face-to-face interviews tend to be higher than
mailed questionnaires. More complex questions are also possible in face-
to-face and telephone interviews.
Interview as Measurement
Telephone and face-to-face interviews allow greater flexibility in presenting
information to respondents. The research design for interview schedules is
similar to mailed questionnaires but includes additional issues of complex-
ity of questions, response biases in interview situations, and monitoring
interviewer progress. The general procedures for structured interviews
involves:
1 Creating or selecting an interview schedule (set of questions, statements,
pictures) and a set of rules or procedures for using the schedule
2 Conducting the interview
TABLE 4.6 Sample questionnaire and coding column
For official use only
Ident.______ ______ ______1^3
Q1 What type of dwelling is this residence?
______ 4
1 Separate house, semi-detached, row/terrace, townhouse, etc.
One storey ( )
Two or more storeys ( )
2 Unit/Flat
In a one or two storey block ( )
In a three or more storey block ( )
3 Other (Please specify). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ( )
Q2 Is anyadult currently studying?
Yes ( ) ______ 5
No ( )
Q3 What is your household's annual income?
Less than $3,000 ( ) $50,001^ $60,000 ( ) ______ 6
$3,001^ $5,000 ( ) $60,001^ $70,000 ( )
$5,001^ $8,000 ( ) $70,001^ $80,000 ( )
$8,001^ $12,000 ( ) $80,001^ $90,000 ( )
$12,001^ $16,000 ( ) $90,001^ $100,000 ( )
$16,001^ $20,000 ( ) $100,001^ $120,000 ( )
$20,001^ $25,000 ( ) More than $120,000 ( )
$25,001^ $30,000 ( ) Prefer not to say ( )
$30,001^ $35,000 ( ) Not applicable ( )
$35,001^ $40,000 ( )
$40,001^ $50,000 ( )
Q4 How many radios are there in this dwelling? (. . . . . .) ______ ______7^8
86

3 Recording the responses
4 Creating a numerical code (a scale or other system of numbers into
which the recorded responses are to be translated)
5 Coding the interview responses.
The general goals of interviewing are to create a positive atmosphere, ask
the questions properly, obtain an adequate response, record the response
and avoid biases. Interviewer bias includes attitudes, interviewer character-
istics (e.g. age, sex, ethnic background) and interviewer perceptions of the
situation.
Figure 4.7 shows the competing forces at play in the interview situation.
From the interviewee's perspective, press of competing activities, embar-
rassment at ignorance, dislike for content, and fear of consequences in
answering in the wrong way are at a maximum in an interview situation.
The research design should maximize the forces that are at a minimum.
Understanding frame of reference and good design are, of course, factors
that maximize those forces.
A pilot study ± a preliminary test of a questionnaire or interview sched-
ule ± helps to identify problems and benefits associated with the design. It
also helps the researcher to get a better understanding of the frame of
reference relevant to the questionnaire and question wording. Figure 4.8
provides a checklist for questionnaire design.
Good design, measurement and administration of a questionnaire or an
interview schedule reduce bias and possible errors. These are the keys to
enhanced construct and internal validity.
VALIDITY
A `method' is not a neutral framework ± it embodies the procedures you use
to collect and analyse evidence. We could apply the method and get bad
results. We could apply it again and get the same bad results. Our methods
Max. Press of competing Embarrassment at Dislike for Fear of
activities ignorance content consequences
Liking for interviewer Prestige of researcher Self-image as Loneliness
dutiful citizen
FIGURE 4.7 Factors affecting people's motivation to provide complete and accurate information
to the interviewer (adapted from Cannell and Kahn,1968: 539)
87

might be reliable, therefore, but not valid. Issues of validity are a part of
research design.
Detectives have an interest in whether clues are real clues and whether
clues really do solve the problem they are studying. Do the clues represent
what you think that they represent? William of Baskerville, the monk-detec-
tive in Umberto Eco's book, The Name of the Rose, was expert at identifying
clues but, as this discussion with Adso, his subordinate novice, shows, he
was not so confident about his judgements about the overall meaning of the
clues.
`But master,' I ventured, sorrowfully, `you speak like this now because you are
wounded in the depths of your spirit. There is one truth, however, that you
discovered tonight, the one you reached by interpreting the clues you read over
the past few days. Jorge has won, but you have defeated Jorge because you
exposed his plot . . . `
`There was no plot,' William said, ànd I discovered it by mistake.'
The assertion was self-contradictory, and I couldn't decide whether William really
wanted it to be. `But it was true that the tracks in the snow led to Brunellas,' I said,
ìt was true that Adelmo committed suicide, it was true that Venantius did not
drown in the jar, it was true that the labyrinth was laid out in the way you
imagined it, it was true that one entered the finis Africae by touching the word
``quatuor,'' it was true that the mysterious book was by Aristotle . . . I could go on
listing all the true things you discovered with the help of your learning . . . `
Ì have never doubted the truth of signs, Adso; they are the only things man has
with which to orient himself in the world. What I did not understand was the
relation among signs. I arrived at Jorge through an apocalyptic pattern that
seemed to underlie all the crimes, and yet it was accidental. I arrived at Jorge
seeking one criminal for all the crimes and we discovered that each crime was
committed by a different person, or by no one. I arrived at Jorge pursuing the plan
of a perverse and rational mind, and there was no plan . . .' (Eco, 1980: 491±492).
Designing Questions
- purpose of questions
- wording and language
- sequencing
Measuring Questions
- categorization
- coding
- scales and scaling
- validity and reliability
Administration
- appearance of questionnaire
- length of questionnaire
- introduction to participants (and ethics statement)
- instructions for completion
- pilot
- follow-up with non-responses
Questionnaire
FIGURE 4.8 Checklist for questionnaire design
88

In social science research, just as in detective fiction, what you think you
have got right at one level may be wrong at another level. You might find a
specific clue and understand its local significance but get the big picture
wrong. We want our conclusions to be valid and reliable. Validity in quan-
titative research is the extent to which your measures do, in fact, measure
the constructs of interest to the research. If I tell you that I have measured
`sex' by `black' and `white', then you would quite rightly tell me that you
have problems with the validity of my definitions. You will tell me that
black and white do not measure sex.
There are three major kinds of validity: construct validity, internal valid-
ity and external validity. Construct validity is the extent to which your
constructs are successfully operationalized and represent the phenomenon
you want to study. Internal validity is the extent to which your research
design really allows you to draw conclusions about the relationship
between variables. External validity is the extent to which your sample is
genuinely representative of the population from which you have drawn it.
Table 4.7, adapted from Judd et al. (1991: 55), provides a good example of
what happens when a test is not measuring what it is supposed to measure.
For example, in Operational Definition 1 we have given an English
(untranslated) IQ test to French students. In Operational Definition 2 we
have provided a translation. In Operational Definition 3 we have provided
the test through interviews. Jacques, as you can see, did well under the
English IQ test. The reason? He was probably good at English. There is,
however, consistency between the second and third measures. The main
sources of bias and error in the measurements are knowledge of English
in measure 1 and conversational skills for measure 2. Robert, for example,
did better in the French translation of the IQ test compared with his inter-
view. It is likely that it was the interview that affected his ability to do the
IQ test.
Maximizing construct validity and internal validity ± ensuring that our
measures do, indeed, measure what we say they do ± reduces the error and
TABLE 4.7 Rankorderof Frenchhighschool students'intelligencescoresobtainedwith
three hypothetical measures
Operational Operational Operational
Definition1 Definition 2 Definition 3
English IQ test French translation French interviews
Jacques Pierre Pierre
Carole Marie Marie
Marie Jeanne Jeanne
Marianne Jacques Jacques
Lisa Lisa Lisa
Pierre Carole Carole
Jeanne Robert Marianne
Robert Marianne Robert
89

the bias that might affect our conclusions. Research studies can use poor
operational definitions and still be reliable ± give us consistent results ± but
not be valid. We want reliability in our study, but reliability should not
come at the cost of validity.
Experiments in particular seek to maximize internal validity. However,
experiments are also susceptible to their own problems of internal validity.
There may be testing or ìnstrument' effects, where the test materials them-
selves might affect what people do. There are also maturation effects, where
time may affect the nature of the experiment. Let's look at òrder effects' and
`carry over' effects as an example (Davis, 1995: 63±64). Tasks in an experi-
ment which are completed serially, one after another, can create òrder
effects'. A person is quite likely to gain experience with the nature of the
task. If the performance of one task carries over to another task in an experi-
ment, then there may also be `carry over' effects.
Davis (1995: 64) uses a Piagetian experiment to demonstrate the differ-
ence between order and carry-over effects. In one Piagetian experiment,
children under the age of five often report that the number of objects in a
row actually increases simply because an adult (acting as experimenter)
spreads the row of objects out so that the row appears longer. If the experi-
menter next uses a teddy bear to spread the row of objects, however, the
children do not say that the number of objects has increased. If the teddy
bear is used first in the experiment to spread the objects, then the children
are more likely to give correct responses: ìt is not that children show an
improvement from first to second task but that they show improvement
only with a particular sequence of conditions' (1995: 64). The carry-over
effects in this case are of interest because they affect the experiment.
However, they are also of theoretical interest.
Internal validity addresses problems in operational definition and the
relationships between variables. Problems associated with sampling, how-
ever, raise a different set of problems. External validity is associated with
sampling. Procedures for sampling enhance external validity.
EXTERNAL VALIDITY AND SAMPLING
Sampling in social science research is a technique, a procedure, for selecting
a subset of units of analysis from a population. Good sampling achieves
representativeness. Detectives in detective fiction are always trying to judge
representativeness ± for example, whether the crook they are looking for
belongs to a typical class of crook or that a particular character is represen-
tative of a particular kind of behaviour. In Chandler's Lady of the Lake,
Marlowe is quick to offer his judgements about whether particular kinds
of behaviour are stereotypical, even when those judgements have an under-
tone of sexism: Ì get a very vague idea of Mrs. Kingsley ± that she is young,
pretty, reckless, and wild. That she drinks and does dangerous things when
she drinks. That she is a sucker for the men and might take up with a
90

stranger who might turn out to be a crook. Does that fit?' He [Mr. Kingsley]
nodded. `Every word of it' (Chandler, 1944: 23).
Working out whether a sample is the right sample is not a simple matter
in quantitative research. You need to decide what your population is and
whether each element of that population can be identified and listed.
Population and Sampling Frame
Constructs are defined and measured by the social scientist. Samples, sim-
ilarly, are defined and measured by the social scientist. The social scientist
uses statistics to make judgements, inferences, about the phenomenon that
he or she is studying. The social scientist uses samples and sample statistics
to make inferences about the populations from which they are drawn.
Populations are operationally defined by the researcher. They must be
accessible and quantifiable and related to the purpose of the research. `All
households in London' is a definition of a population, with households as
the unit of analysis. But what is a `household'? Is it any dwelling, including
the boat in the backyard that your brother lives in? Is it Buckingham Palace?
If all of these examples are `households', then these need to be included in
the definition of the population. If a sample of households was drawn from
London, then `London' needs to be defined. Is London defined by local
council boundaries? Is it defined by census boundaries?
When you have decided on all these definitions, then every household in
London that you have defined as a household belongs on your list. That list
is called a sampling frame.
Simple Random Sampling
You can number each household, if you wish, and put them in a hat (a big
hat in this case). Let us say that you drew out 10 households (a sample). You
know that there was no bias in your choice. Each element, each household,
in your sampling frame had an equal chance of being chosen. This is called
a probability or random sample. You could also use a table of random
numbers. For example, a researcher who wants to analyse 15 households
out of 100 households would number each household from 00 to 99. The
researcher would then select 15 numbers from a table of random numbers,
such as the truncated listing in Table 4.8. You can start anywhere in the table
of random numbers and then proceeding up, down or diagonally, select the
15 numbers needed. In this case, the selection starting from 28 downwards
would be 28, 36, 77, 17, and so on.
By chance, however, we might find that all 15 households you pulled
from the hat are boats. We have not represented all households, only
boats. In the study we may require, therefore, stratified random sampling.
We break up the sampling frame into different strata and then conduct a
simple random sample.
91

Stratified Random Sampling
We could split up households in the list by type of household into single-
level households, double-level household, boats, and other classifications.
There may be very few boats-as-households in the population ± 10 per cent.
If we wanted to represent that 10 per cent in our sampling, then 10 per cent
of our sample would be boats. This is a proportionate stratified random
sample, where we represent each type of household proportionately. A
simple random sample from each separate list of types of household
would be required. Sometimes we might want to over-represent a particular
stratum, especially if there are very low numbers. For example, you might
decide that people living on boats are of special interest. This is dispropor-
tionate stratified random sampling.
Multi-Stage Cluster Sampling
Large-scale, national studies often use a form of cluster sampling called
multi-stage cluster sampling. Normally we select one unit at a time in
probability sampling. This requires a complete list of the units of analysis.
Sometimes there is no way to create a list. In these cases we use a procedure
known as cluster sampling. In cluster sampling we select groups or cat-
egories. For example, following Figure 4.9, we can break London up into
suburbs and randomly sample those suburbs. We could then break up those
suburbs into census collectors' districts (about 400 households) and then
randomly select those districts. We could then select streets and system-
atically sample those streets. A systematic sample is when every nth unit of
analysis is selected ± every second house in the street, for instance. Once we
have selected our sample of households, we would then select our demo-
graphic quota from those households (people of a certain age or sex, etc.). In
order to randomly select our participants we could again use a table of
random numbers designed for this purpose (Table 4.9). For example, the
interviewer could ask `How many people are there in your home aged 15 or
older?' If the first participant says `three people', then according to Table 4.9
the second oldest person is chosen.
Simple, stratified and multi-stage cluster sampling are all forms of prob-
ability sampling. Going to a shopping mall and talking to a person whom
you think would be useful for your study is NOT random sampling ± that
person did not have an equal and known chance of being selected.
Why do we need probability sampling? Good sampling reduces the
chance that we have picked the wrong people or unit of analysis for our
TABLE 4.8 Table of random numbers
2 8 4 9 8 8 9 9 5 5
3 6 1 9 0 3 0 1 1 1
7 7 9 9 7 8 3 3 3 2
1 7 6 9 2 4 1 8 6 7
92

study. Good sampling reduces error and maximizes external validity. The
statistics we use for analysis of samples also require probability sampling.
Statistics that make judgements about the relationship between samples
and their population are called inferential statistics. We will talk about
inferential statistics in Chapter 6.
Table 4.10 provides a summary of the probability sampling procedures.
Simple random sampling is good where there is a high degree of homo-
geneity in the defined population. Stratified random sampling is good
where there is a high degree of heterogeneity. Cluster sampling is an
economical way to get access to populations, but increases error because
we are dealing with groups.
Sample Size
A large sample is no guarantee of accuracy. The Literary Digest in the
United States regularly polled its readers between 1916 and 1932 and it
Victoria Street
23 25 27
FIGURE 4.9 Multi-stage cluster sampling ^ following the census tracts
93

regularly picked the winners of presidential elections. The magazine
mailed out ballots to over 10 million residential telephone users and, in
later years, car owners. The size of the sample was thought to explain
its success and was often called ùncanny', àmazingly accurate', and
ìnfallible' (Hunt, 1985: 122). In 1936, however, the Literary Digest's
reputation suffered a blow: 2,376,523 ballots said that Franklin Roosevelt
would get only 41 per cent of the vote. In fact Roosevelt got 61 per cent of
the vote.
The sample, in this case, was drawn from an unrepresentative group ±
those who had telephones and cars. The Gallup and Fortune surveys came
close to the final result because they tried to sample proper proportions of
people at every social and geographic level.
In simple experimental research with strict controls, successful research
may be conducted with samples as small as 10 to 20 in size. In most experi-
mental research the use of samples of 30 or larger is recommended. In
multivariate research the sample size should be several times (more than
10 times) as large as the number of variables. There are few occasions in
behavioural research where samples smaller than 30 or larger than 500
in size can be justified. The more complex your study, of course, and the
more complex your requirements, the more expensive your sampling is
going to be.
TABLE 4.9 Random selection of households for interview
No. of people in household
1 2 3 4 5
Person to interview 1 2 2 4 3
1 1 2 5
3 1 4
3 1
2
TABLE 4.10 Summary of sampling procedures
Design Description Benefit
Simple random All units of analysis are known and Generalizability of findings
each have an equal chance of
selection
Stratified random Population is divided into strata Most efficient of the designs
and units then selected:
Proportionate In proportion to the original strata Sampling frame for each stratum required
Disproportionate Based on criteria where different Good for representing strata that have
proportions may be required small numbers
Cluster sampling Based on groups or geographical clusters Costs of data collection reduced, but
with all members in each cluster randomly increased chance of error
selected
94

Non-Probability Sampling
Not all populations defined by a researcher are easily accessible or easily
quantifiable. For example, `all heroin users in the United Kingdom' is an
operational definition for a particular kind of population, but it is unlikely
that you could find them all or list them all (a sampling frame). You could,
of course, define your population as `all convicted heroin users in British
prisons', in which case the establishment of a sampling frame becomes
more feasible (assuming ethics approval).
Researchers who cannot ensure that every unit in their population has an
equal chance of being selected, or who simply don't need a sampling frame,
often use non-probability techniques. The major non-probability techniques
are judgement, opportunistic and snowball sampling. Judgement sampling
involves the selection of the units of analysis according to criteria estab-
lished by the researcher (e.g. age, sex, occupation). The researcher still
requires a detailed knowledge about the `population'. Opportunistic sam-
pling relies on selection of those most likely to cooperate with the researcher.
Not surprisingly, opportunistic sampling is difficult to replicate. Snowball
sampling relies on the researcher's knowledge of the situation and the
people he or she knows. The researcher contacts people relevant to him
or her. Those people then contact people they know, and so on. There is
also theoretical sampling where the researcher chooses the situation, events or
people according to some theoretical purpose (Burgess, 1984: 55±56).
Trade-Offs
There can be trade-offs between different types of validity. Classical labor-
atory experiments maximize internal validity, because they want to establish
causation, but minimize external validity, because laboratory settings are
not, by definition, natural settings. Decisions on which method to choose
will depend, therefore, on what you want to achieve, as Figure 4.10 shows.
Triangulation
Combining different methods ± quantitative and qualitative ± to study the
same phenomenon has been called triangulation. Norman Denzin (1970)
said that triangulation involves not only the combination of methods and
data, but of theories as well. He said that there are four types of triangula-
tion, including:
1 data triangulation ± where the researcher estimates the impact of time,
space and different types of interaction (individual, group, and collec-
tive) on the data;
2 investigator triangulation, where more than one person examines the
same situation;
3 theory triangulation, where alternative or competing theories are used;
95

4 methodological triangulation, where the same method is used on differ-
ent occasions.
Paul Lazarsfeld, the mathematical sociologist, was one of the earliest
advocates of combining methods. He and his colleagues attempted to maxi-
mize internal and external validity by conducting a natural experiment ± a
field experiment ± in the 1940s and combining that experiment with other
methods. Lazarsfeld's study could not be conducted in a laboratory setting
because it examined voter intentions and voter behaviour. These phenom-
ena are best studied in their natural setting ± a political campaign.
GREAT MEDIA AND POLITICS DETECTIVE STORIES: Using Survey
Data. Do media change people's political attitudes? The People's
Choice (Paul Lazarsfeld)
Paul F. Lazarsfeld . . . virtually created the fields of mathematical sociology, multivariate
survey analysis, and the empirical study of both voting behaviour and mass commun-
ications
David L. Sills (Rogers, 1994: 244)
Paul Lazarsfeld, a methodologist, joined the Columbia Department of
Sociology in 1941. Robert Merton, a theoretician, joined the Department at
the same time. Both became famous for developing survey and interview
methodology. Merton, the theorist, became expert at interview meth-
odology and first used the words `focused interview' and `focused group'
and developed the techniques. Lazarsfeld, the methodologist, became
expert at media theory and revolutionized media theory and our under-
standing of how public opinion works.
Use field experiment
No
Internal validity most
important?
Yes
Use laboratory experiment
Use a laboratory and
a field experiment
Internal and external validity
important?
Yes
FIGURE 4.10 Experimental choice based on issues of internal and external validity
96

Lazarsfeld's collaboration with Merton stands in stark constrast to his
collaboration with Theodore Adorno. Adorno, the Jewish neo-Marxist
Frankfurt School scholar, was interested in the conditions that lead to pre-
judice and persecution (Adorno had escaped from Nazi Germany). Adorno
drew a distinction between àdministrative research', which served govern-
ment and industry (and which he said described Lazarsfeld's research at
the time), and `critical research', which sought to critique the whole cap-
italist enterprise and the role of ideology in that enterprise. For Adorno,
administrative research could be manipulative and at the service of power-
ful interests. Critical research was a necessary correction. While Adorno
was opposed to quantitative research as ìnstrumental' and `manipulative',
he used it himself in his famous study The Authoritarian Personality. `How
can one say with assurance that the numerous opinions, attitudes, and
values expressed by an individual actually constitute a consistent pattern
of organized totality? . . . There is no adequate way to proceed other than by
actually measuring, in populations, a wide variety of thought contents and
determining by means of standard statistical methods which ones go
together' (Adorno et al., 1950: 3). Judgements about the significance of
the statistics, says Adorno, can only be made òn the basis of theory'
(1950: 3).
The 1940s at Columbia University are a snapshot of the quantitative
versus qualitative divide, the study of power as ideology (Adorno) versus
the study of influence as the result of many counter-acting variables
(Lazarsfeld) and the difference between European and American
approaches to the study of communication and sociology. Lazarsfeld,
Merton and Adorno were (and remain) a microcosm of the key debates in
sociology and methodology.
Adorno and Lazarsfeld shared a common interest: democratization of
methods of research ± making research methods transparent; and hybridity
± making sure that qualitative research informed quantitative research.
Lazarsfeld, Berelson and Gaudet's classic work People's Choice (1944) is a
classic example of hybridity and the creation of a new survey research
method to assist with explanatory research.
Methodology and Theory
`We are interested here in all those conditions which determine the political
behaviour of people. Briefly, our problem is this: to discover how and why
people decided to vote as they did. What were the major influences upon
them during the campaign in 1940?' (Lazarsfeld et al., 1944: 1). These open-
ing sentences provide a simple and clear overview of the aims of People's
Choice. The 1940 presidential election in the United States presented an
opportunity to undertake a study of voting intentions in a way not done
before.
Previously, voting records were the major material used for analysis of
voting behaviour. It enabled the study of the geographical distribution of
97

voting results. University of Chicago researchers in an ècological analysis'
combined the results of voting with the census data on voters (for example,
what the voting patterns might be in predominantly Irish districts). Public
opinion polls went a step further by relating political opinion to the char-
acteristics of the individual voter. But these polls were normally conducted
with different people and not the same people over time.
Never before had a person's voting intentions been traced through the
course of a political campaign. Lazarsfeld used the panel technique ± the
same set of voters over the period of the political campaign and election ± to
study voting intentions. Lazarsfeld's theoretical interests were, therefore,
twofold ± to investigate key influences on voting behaviour and to create
a new research method to do so.
Method
Hypotheses and Operationalization
Lazarsfeld had a range of specific research questions he wished to address,
such as `What is the effect of social status upon vote?' `How are people
influenced by the party conventions and the nominations?' `What role does
formal propaganda play?' `How about the press and the radio?' `What of
the influence of family and friends?' `Where do issues come in, and how?'
`Why do some people settle their vote early and some late?' Ìn short, how
do votes develop? Why do people vote as they do? By inference and by
direct accounts of the respondents, we shall try to show what influences
operated . . .' (Lazarsfeld et al., 1944: 6±7).
Lazarsfeld and his colleagues had specific variables in mind for these
research questions, although they held off on premature judgements
about which variables had significant influence. Erie County was chosen
for the study `because it was small enough to permit close supervision of
the interviewers; because it was relatively free from sectional peculiarities,
because it was not dominated by any large urban center, although it did
furnish an opportunity to compare rural political opinion with opinion in a
small urban center' (Lazarsfeld et al., 1944: 3). Three thousand people were
chosen to represent the County. Every fourth house in the County was
visited by trained local interviewers, mainly women. Four groups of 600
persons were selected by stratified sampling. Of the four groups, only three
were re-interviewed once each. These groups were used as `control groups'
to test the effect that repeated interviewing might have on the panel
(Lazarsfeld et al., 1944: 3). The fourth group, the panel, was interviewed
once each month from May to November 1940.
Lazarsfeld's interests were multivariate and `nomothetic'. He was inter-
ested in many variables and how they interrelate and influence one another.
However, he was also very interested in the ìdiographic' side of the survey
research and direct accounts from participants. Whenever a person changed
his or her vote intention in any way, from one interview to the next, detailed
information was gathered on why he or she had changed. The following
98

narrative on the history of a single voter's intentions over the course of the
political campaign gives an idea about how serious Lazarsfeld and his
colleagues were in combining aggregated data with individual accounts.
This young man, undecided in May, voted for Roosevelt in November. But it
would be incorrect to assume that at some point during the campaign he simply
made up his mind once and for all. Actually, he followed a devious route on his
way to the polls. He was a first voter with some high school education and with a
slightly better than average socio-economic level. At first he favored Taft for the
Republican nomination because he was a fellow resident of Ohio, but on the other
side of his indecision was his tendency to vote Democratic `because my grand-
father is affiliated with that party.' This tendency won out in July when he
announced that he would vote for Roosevelt to please his grandfather. In
August, however, his opposition to the President's stand on conscription gained
the upper hand and he came out for Willkie, even though he knew little about
him. At this point his vote intention represented a vote against conscription and
Roosevelt's pressure for it. At the same time, he generalized this disapproval of
conscription into a disapproval of the third term. The following month he changed
again: he simply did not know enough about Willkie to cling to him so he reverted
to a state of indecision and began to think that he would not vote at all. This
attitude persisted throughout the last days of the campaign, when he indicated
that the outcome of the election did not make any difference to him. During
August and September he believed Willkie would win but later he was undecided
on that too, partly because a movie audience had booed the Republican candidate
in a newsreel appearance a few days before. But on Election Day, he voted for
Roosevelt. He was repelled at the very end of the campaign by what he considered
Willkie's begging for votes and he was strongly influenced by fellow workers at
the foundry where he was employed. The saga of the formation of his vote illus-
trates the kinds of data not available before the development of the repeated
interview technique. (Lazarsfeld et al., 1944: 5±6)
The quantitative variables of the research in People's Choice ranged from
social and economic status to religious affiliation and age and various
indexes on political predisposition, breadth of opinion, magazine reading,
radio listening and general or overall exposure to the campaign, political
exposure bias, and agreements with arguments of either side.
Operationalization of `social and economic status' gives you some idea
about how Lazarsfeld and his colleagues went about quantification.
Interviewers were trained to assess the homes, possessions, appearance,
and manner of speech of members of the sample and to classify them
into their proper stratum in the community according to a set quota. `The
people with the best homes, furniture, clothes, etc., i.e., the ones with the
most money, would be classed as As; and the people at the other extreme
would be Ds. In Erie Country, the quote was approximated in the following
distribution: A, 3%; B, 14%, C‡ 33%; C7, 30%; and D, 20%' (1944: 17).
Lazarsfeld and his colleagues had simple and complex measurements.
For magazine reading, the respondent was asked about several specific
articles appearing in current issues of magazines. This index was simply
99

a count of the number of articles on political affairs that the respondent
reported reading. In the October interview each respondent was asked
whether he or she agreed with eight arguments then current in the political
campaign. For example, one of the eight arguments was `Roosevelt has
great personal attractiveness, capacity for hard work, and keen intelligence'.
A person who agreed with an argument supporting his or her own side or
disagreed with an argument supporting the opposition received a +1 score
and a person who disagreed with his or her own argument or agreed with
the opposition's argument received a 71 score for each question. Each
individual could score between 78 and ‡8.
Variables
The People's Choice study found that variables such as social and economic
status, affiliation with `business' or `labour' and religious affiliation were
good predictors of voters' intentions. Figures 4.11 and 4.12 provide an over-
view of the results on business and labour affiliation and religious affiliation
and their relationship to party choice.
One of Lazarseld's key findings was that mass media appeared to have
little influence changing people's minds. It had a reinforcement effect. `The
first thing to say is that some people were converted by campaign propa-
ganda but that they were few indeed' (Lazarsfeld et al., 1944: 94). An unex-
A+B C+ C- D
Business Labour Business Labour Business Labour Business Labour
(75) (16) (80) (105) (53) (104) (10) (85)
Democrats Republicans ( ) Total cases
38%
25%
20% 53% 47% 66% 70% 73%
FIGURE 4.11 Whereas actual occupation does little to refine the relationship between SES level and
vote, it makes more difference whether a voter considers himself as belonging to`business'or `labour'
(adapted from People's Choice)
100

pected finding emerged. `Whenever respondents were asked to report on
their recent exposures to campaign communications of all kinds, political
discussions were mentioned more frequently than exposure to radio or
print' (1944: 150). Those most likely to change their vote in the political
campaign `read and listened least' (1944: 95). Opinion leaders, such as the
workers at the foundry in the case of the young man cited earlier, had the
most significant influence on outcomes. Mass media did not change be-
haviour because `the people who did most of the reading and listening not
only read and heard most of their own partisan propaganda but were also
most resistant to conversion because of their strong dispositions' (1944: 95).
This resistance was also reinforced by the people around them. This recogni-
tion of the role of personal influence as a mediating factor in mass-media
influence led to a complete reconsideration of the nature of mass-media
influence. Early models of mass-media influence had assumed a simple
cause and effect. Figure 4.13, adapted from Communication Models (1981),
graphically represents this `hypodermic' or stimulus±response assumption
about mass media. Individuals receive messages and act on them.
Figure 4.14 shows graphically the effect of Lazarsfeld's work on assump-
tions about the `receiver'. Lazarsfeld and his colleagues argued that a `two-
step' model of communication was most appropriate to explain mass-media
A+B C+ C- D
Protestant Catholic Protestant Catholic Protestant Catholic Protestant Catholic
(269) (42) (413) (134) (386) (113) (217) (76)
Democrats Republicans ( ) Total cases
34%
71%
24% 75% 46% 77% 57% 86%
FIGURE 4.12 Religious affiliation splits the vote sharply. This cannot be attributed to the fact that
Catholics in this county are, on average, lower in SES level than Protestants. The relationship between
vote and religious affiliation holds true on each SES level.
101

influence. The vote decisions of 70 per cent of the people, whether or not
they expressed an early vote intention, corresponded to the vote tendencies
prevailing among groups with social characteristics similar to their own.
Social groups, therefore, were a major influence on voting intentions and
voting behaviour.
People's Choice demonstrated how sophisticated survey data could get
and how the collection of quantitative survey data over time can be com-
plemented with qualitative data. Lazarsfeld was a strong advocate of
hybridity ± the combining of quantitative with qualitative methods. He
concluded that:
1 any phenomenon should be measured with objective observations as
well as with introspective reports;
2 case studies should be combined with statistical information;
3 data gathering should be combined with information about the history
of what is being studied;
4 data from unobtrusive studies (e.g. observation) should be combined
with questionnaire and other self-reported data (Rogers, 1994: 285).
Individual
Mass Media
FIGURE 4.13 One-step model of mass-media influence
Opinion Leader and Groups
Mass Media
FIGURE 4.14 Two-step model of mass-media influence
102

SUMMARY
The ability to recognize what counts as evidence, what counts as clues, is
closely related to the sophistication of a research design and its data collec-
tion techniques. Umberto Eco's character William of Baskerville got indi-
vidual clues correct but was mistaken about their overall causal
significance. Social science has the same problem. Causality is not easy to
establish.
The idea of `causation' is approached with care by quantitative research-
ers. Causation and correlation are not the same. Correlation of variables
does not establish causation. The idea that causes can be easily established
in social science research is wrong. Many of the phenomena a social scien-
tist wishes to study cannot be placed into a laboratory context because (1) it
is ethically not possible to manipulate the independent variable or (2) the
independent variable in its natural setting cannot be replicated in a labor-
atory environment.
Experimental methods seek to isolate causes and to maximize internal
validity. Experiments intend to explain and have a theoretical purpose in
mind. There are two major types of experimental design. Between-subject
designs compare groups exposed to the independent variable with control
groups that are not exposed. Within-subject designs expose the same
groups to the independent variable at different times and the individuals
themselves act as a control. Experiments should be used when the
researcher is certain that causality is an issue and that the hypothesis is
appropriate to experimental research.
Survey methods make possible analysis of large populations and may be
exploratory, descriptive or explanatory. `Populations' are analytically
defined by the social scientist. A `sampling frame' is a list of all members
of the researcher's population and can be used to draw a random sample.
Questionnaires in surveys use standardized questions. This is an advantage
because it is cost effective and relatively quick. However, failure to address
the participants' frame of reference can affect the validity of a questionnaire.
Social context can affect interpretation of the simplest questions.
All quantitative research methods are subject to bias and error. There is
often a trade-off between internal and external validity. Experiments maxi-
mize internal validity and surveys maximize external validity. Modern
social scientists often combine methods in order to maximize both.
Lazarsfeld and his colleagues addressed construct and internal validity
by combining qualitative and quantitative understanding of their partici-
pants. People's Choice refined the panel technique and attempted to isolate
the major influences on voting behaviour by examining the same people
over time. People's Choice is interested in causality but the topic was not
appropriate for laboratory research. It is not possible to replicate a presi-
dential campaign in a laboratory setting. Nor is it possible to manipulate the
independent variable in the natural setting ± for example, to manipulate
103

political campaign propaganda or to change the characteristics of a pres-
idential candidate's personality to see if it made a difference. People's Choice
did establish a control group to check on interviewer effect and isolated as
many of the significant variables as possible.
People's Choice is also an example of a quantitative study that is more
`inductive' than `deductive', at least in its initial design. People's Choice starts
with methodology and general research questions, collects data and then
works towards theory. Hofstede's study, described in Chapter 3, starts with
theory that informed the methodology and the collection of data. Figures
4.15 and 4.16 provide an overview of the differences between the two
approaches.
A choice of an inductive or deductive approach depends upon the
research topic and the researcher's interests. Both Lazarsfeld and
Hofstede were interested in quantitative and qualitative data.
We have investigated many of the issues associated with basic research
design and many of the issues associated with operationalization. Now
it is time to turn from research design to data analysis. Decisions on
research design and methodology affect what counts as evidence ± as
clues. But there is also the world of statistical analysis that complements
research design. The statistical sleuth ± the data snooper ± can identify
Methodology
Collect Data
Theory
FIGURE 4.15 Inductive approach
Theory
Methodology
Collect Data
FIGURE 4.16 Deductive approach
104

patterns, regularities and irregularities, in data that are relevant to a study.
Numbers tell a story.
MAIN POINTS
. Quantitative methods require detachment of the observer, especially in
experimental method where personal involvement can affect the out-
comes of the research (unless that effect is accounted for). Personal
involvement of the researcher in collecting data, however, is appropriate
in a range of research designs.
. There are three main methods of research ± case study, survey,
and experiment. All three methods can employ different data collection
techniques, including questionnaire, interview, content analysis,
observation.
. Experimental method involves manipulation of the independent
variable and direct observations of the effects of that variable.
Between-subject and within-subject designs are the two basic designs
in experimental research. Field experiments investigate independent
variable(s) in the `natural' environment.
. The idea of `causation' captured the popular mind early in the 20th
century. Establishing causation, however, involves skill in controlling
extraneous variables. Genuine experiments are modest in their
conclusions and relate to very specific issues associated with a hypo-
thesis.
. Survey method is appropriate when you cannot observe directly what
you want to study. Survey method is particularly appropriate for large
populations. Self-administered questionnaires and interview schedules
are two of the common techniques of data collection within survey
method. Both entail standardization of questions.
. Frame of reference ± understanding of the social context in which the
survey is to be conducted ± is essential to the success of surveys. Frame
of reference includes especially the language used by the participants
and their understanding of the meanings attached to questions.
. Questions in quantitative questionnaires must be designed with levels of
measurement in mind. The level of measurement will affect what kinds
of statistical analyses are appropriate. There are two main types of
question ± closed-ended and open-ended. Closed-ended questions
give the participant fixed choices, including a preference not to reply.
Open-ended questions may be post-coded by the researcher, where
appropriate.
. Multiple-item scales provide a more complex view of underlying
attitudes. Summative scales, such as the Likert, are among the most
commonly used attitude measures.
105

. Construct validity and internal validity address problems of operational
definition and the relationships between variables. Do our measures
really measure what they say they measure?
. External validity addresses problems with sampling. Probability sam-
pling assumes that each member of the defined population has an equal
chance of being chosen. Simple random sampling and stratified sam-
pling are two of the most common forms of probability sampling. They
maximize external validity.
REVIEW EXERCISES
1 Visit the research ethics site of a university on the internet and
download, or examine, their ethics requirements for experimental
and survey research. What are the limitations on human experi-
mentation?
2 Create five hypotheses appropriate for an experimental design.
3 Read Stanley Milgram's (1974) Obedience to Authority: an experi-
mental view (New York: Harper and Row), or an experiment of
interest to you. What were the independent variables?
4 Create a survey design and address the following issues:
(a) What is the purpose of the survey?
(b) What is the hypothesis(es)?
(c) Are operational definitions necessary?
(d) Create 15 questions relevant to the survey.
(e) Design a cover letter.
5 Create your own seven-point Likert scale to test a Machiavellian
personality.
6 Which sampling technique is most appropriate for the following
studies?
(a) A study to establish the demographic make-up of an audience
for local radio.
(b) A study on teenage use of the internet.
(c) A study on alcoholism in New York.
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108

5
`DATA! DATA! DATA!'
Analysing data from the inquiry
'Data! data! data!' he cried impatiently.
'I can't make bricks out of clay'
Sherlock Holmes,
The Adventure of the Copper Beeches
`Data' never comes to the social scientist clean, like cement for bricks. As we
found in Chapters 3 and 4, the society a person lives in ± and a person's
beliefs ± can directly affect what counts as a `clue' and what counts as
èvidence'. Holmes himself was not entirely free from the racial and gender
stereotypes of his time. Holmes says, for example, that èmotional qualities
are antagonistic to clear reasoning', but he is equally able to proclaim as fact
that `women are never to be entirely trusted' (The Sign of Four). Operational
definitions can be affected by the society we live in. But it is wrong to then
conclude that we can never retrieve useful quantitative data from the study
of psychology or society. Holmes, for all his faults, could see alternative
points of view, even if he did not like them: ìf you shift your own point
of view a little, you may find it pointing in an equally uncompromising
manner to something entirely different' (The Boscombe Valley Mystery).
Recognition of the problems of validity and making sense of common
sense is a good first step in creating a valid and reliable research study.
Always ask to see a person's research design; always ask to see their defini-
tions. The same principle holds for exploring statistical data. Always ask for
the data! Numbers are not neutral ± they form patterns and they tell a story.
LOOKING AT THE CLUES: The Statistical Sleuth
Good detective work involves making sense of the clues, making sense of
the variables, collected. Hercule Poirot, for instance, sometimes guesses
who committed a murder before he has the evidence. Às I say, I was
convinced from the first moment I saw her that Mrs. Tanios was the person
I was looking for, but I had absolutely no proof of the fact. I had to proceed
carefully' (Christie, 1982: 247). Proof of the fact is a part of data analysis in
social science research. Proceeding carefully is exactly what you need to do
when you start trying to make sense of individual clues.

Why Explore Data?
Some research studies have well-defined hypotheses that are tested by the
researcher. Some studies, such as People's Choice, have broad research ques-
tions that invite exploration. In both cases good data analysts plot their data
before they use sophisticated statistical procedures. Graphical displays of
data are one of the most important aids in identifying and understanding
patterns of data and relationships among variables. Indeed Chambers et al.
(1983: 1) go as far as saying that `there is no statistical tool that is as power-
ful as a well-chosen graph'.
Over the past two decades a number of new methods for displaying data
have been developed that allow for more informative examination of data.
Most of these methods belong to a family of techniques known as explor-
atory data analysis (see Tukey, 1977). These tools are particularly appropriate
for the statistical sleuth ± or the `data snooper', ± as Abelson (1995) aptly
put it. The data snooper is an analyst who is vigilant of odd patterns or
irregularities in data. These irregularities may suggest that something
strange is going on ± for example, calculation errors, data entry errors,
data not conforming to distributional assumptions or, in more serious
cases, data that are fraudulent.
Graphs and plots draw out hidden aspects of the data and relationships
among variables that a person may not have anticipated. These `data-driven
discoveries' may spark new investigations previously not considered and
may eventually lead to changes in the theories or hypotheses driving the
original investigation.
Graphs and plots may complement textual material that in turn may
provide a more complete picture of the issue under investigation. Good
graphical representations are also good communication. They are easily
grasped and therefore easily remembered.
PLOTTING DATA
Stem and Leaf Displays
Variables vary and one of the best ways to see how they vary is to use a
stem and leaf display. The stem and leaf display is a quick and easily
constructed picture of the shape of a distribution (Tukey, 1977). You do
not need a high-powered computer to generate one; if you have a piece
of paper and a pencil you can make a stem and leaf display by following
some simple steps.
The basic idea of a stem and leaf display is that the digits that make up
the numerical values are used in sorting and displaying the numbers. The
digit(s) at the beginning of each datum (or leading digits) in a distribution
serve to sort the data; the remaining or trailing digits are used to display the
data. The leading digits are also referred to as stems while the trailing digits
are referred to as leaves.
1
10

A set of very simple rules (based on Moore and McCabe, 1993; Velleman
and Hoaglin, 1981) allows us to construct stem and leaf displays:
1 Separate each value into a stem and a leaf. You will need to choose a
suitable pair of adjacent digit positions for each datum, say, tens digits
and units digits. Usually, stems have as many digits as necessary for
displaying the data appropriately for your purpose. On the other hand,
each leaf usually has just one digit.
2 Construct a column of all the possible sets of leading digits or stems for
the range of values in the distribution in descending order. Draw a
vertical line to the right of these stems.
3 For each score, record the leaf on the line labelled by its stem and
arrange the leaves in increasing order from left to right.
These rules are applied and illustrated in Example 5.1.
Example 5.1: Stem and leaf display
Performance on an arithmetic test is measured in a small class of children.The scores
are as follows:
16 18 14 23 17 13 19 21 16
To construct a simple stem and leaf display we begin by choosing a pair of adjacent
digits. In this case a suitable pair of digits would be the tens digit and the units digit.
For the value16 we would split the value1 (tens digit) and 6 (units digit) where `1'
would be the stem and `6' would be the leaf. Now split each value between the two
digits.We construct a column for the stems and then write the leaves corresponding
to each stem in ascending order.
Stem Leaf
1 3466789
2 13
3
Represents values 21
and 23
An important feature of stem and leaf displays is that they represent all of
the data in the distribution. The data are preserved exactly in the `stem±leaf'
arrangement. It is possible to reconstruct the exact values that are repre-
sented in the display.
DATA ! DATA ! DATA !
1
1
1

In Example 5.1 we defined the leaves associated with each stem to range
from 0±9. Sometimes this range is inappropriate. This is especially the case
when you have lots of data. If we had 1,000 observations that ranged
between 10 and 30, a stem and leaf display based on stems whose leaves
ranged from 0±9 would produce a display with only three very long stems ±
not a very helpful display. One way to accommodate larger datasets and to
obtain a plot that is more meaningful is to `split' the stem and correspond-
ing leaves into smaller segments. For instance, each stem could have two
segments, 0±4 and 5±9. We will use 1. to represent values that lie between 10
and 14, and 1* to represent values that lie between 15 and 19. In other
words, the symbols `.` and `*' denote the leaves 0±4 and 5±9 respectively.
If we apply these new stems to the data in Example 5.1, we then have a new
stem and leaf display that looks as follows:
Stem Leaf
1. 34
1* 66789
2. 13
You can see that we have a different-looking display. The shape of the
distribution has changed. How you split the stem is up to the data snooper.
He or she needs to choose a stem that will best identify the salient features
of the data under investigation.
Stem and leaf displays can also be used to compare two distributions.
Such plots are sometimes referred to as back-to-back plots. For example, we
may be interested in comparing subjective computer experience using the
Subjective Computer Experience Scale among a sample of 10 male and 10
female undergraduate psychology students (Rawstorne et al., 1998). High
scores indicate greater negative computer experience. The data in Table 5.1
are followed by the back-to-back plot.
We can clearly see that the distributions for males and females are differ-
ent. Whether these distributions are statistically different is a question we
will answer in the next chapter.
Visual representations of data can provide us with clues when we suspect
`fishiness' in a set of data. Abelson (1995) cites an example from the cele-
brated Pearce-Pratt studies on tests of clairvoyance (Rhine and Pratt, 1954).
An experimenter (Pratt) turned over decks of symbol cards and recorded
the sequence, while the clairvoyant (Pearce), who sat in another building,
recorded his impressions of what the sequence of symbols had been. A third
party then compared the lists and recorded correct matches. There were five
possible symbols, so the probability of a match by chance was 20 per cent.
However, the reported success rate for matches was 30 per cent ± a statis-
tically significant result!! This was quite an extraordinary result, but one
1
12

that led critic Hansel (1980) to think about other possible explanations,
including fraud! The key observation Hansel made was to note that the
success rate was highly variable. Some days yielded upwards of 40 per
cent correct, but other days only 15 per cent correct. Why? Inspecting the
site on the Duke University campus, Hansel constructed an elaborate
hypothesis of fraud. The receiver Pearce, motivated by notoriety as a pre-
sumed psychic, cheated. `On many of the days, he slipped out of the other
building as the trials began, hid across the hall from Pratt's office, and stood
on a table from which he could see Pratt's symbols through a pair of open
transoms. With enough time to copy some or all of them, he left his hiding
place and simulated an arrival from the other building. On his symbol
sheet, he made sure not to look too perfect, but otherwise produced strong
``data''. Pratt, his back to the transoms, was an innocent party to the decep-
tion' (Abelson, 1995: 82).
A stem and leaf plot of the ESP data got Hansel thinking. The plot is
reproduced in Figure 5.1 and represents successful hits per 50 trials.
Hansel found a gap at around the values 10, 11 and 12 ± the gap where we
would expect a success rate of 20 per cent! The distribution appears to have
two modes ± a cluster for success days and a cluster for failure days! Could
cheating be occurring? Hansel thought so.
Histograms
Stem and leaf displays are useful, but they become cumbersome to con-
struct if you have very large numbers of observations and especially if you
do not have access to a computer. One way of dealing with this problem is
TABLE 5.1 Example of back-to-back plot
Males Females
32 40
45 41
48 60
50 65
55 66
53 55
52 57
45 58
32 67
60 62
Males Females
22 3
855 4 01
5320 5 578
0 6 02567
1
13

to divide the range of values into intervals and report the number (or
frequency) of observations that fall into each interval. Assume you are a
statistics lecturer and you have 100 students enrolled in your introductory
statistics class. Assume also that your students have sat their final exam for
which they can obtain a mark out of 100. Table 5.2 provides the appropriate
layout.
This table is commonly referred to as a frequency distribution. Sometimes it
is more interesting to examine the relative rather than actual frequency of an
interval. The relative frequency of an interval is obtained by dividing the
frequency of the interval by the total number of observations. This fraction
can also be reported as a percentage. Relative frequency distributions
are useful if you wish to compare either parts of the same distribution or
distributions from two or more groups.
2 4
2 333
2 0000001
1 89
1 677
1 445
1 3333
1
0 8889999
0 6
0 55
0 3
A gap in
the data !!
FIGURE 5.1 A stem and leaf display of ESP data (source: Abelson,1995: 82)
TABLE 5.2 Frequency distribution table for grouped data
Interval Midpoint Frequency Relative frequency
90^100 95 5 0.05
80^89 85 8 0.08
70^79 75 15 0.15
60^69 65 25 0.25
50^59 55 36 0.36
40^49 45 8 0.08
30^39 35 3 0.03
20^29 25 0 0.00
1
14

A histogram is a graphical representation of a frequency distribution. The
horizontal axis is broken into segments representing the intervals of the
scores. The vertical axis represents the frequency of observations. Above
each interval on the horizontal axis we draw a bar with height representing
the frequency associated with that interval. An example of a histogram of
the examination marks data is presented in Figure 5.2.
Boxplots
The boxplot is another useful exploratory data analytic technique for repre-
senting data visually. Boxplots are useful because the plot depicts the im-
portant features of the distribution. A very simple way of examining a
distribution is to look at the values that represent:
1 the middle of the distribution (we refer to this value as the median);
2 the smallest (minimum) and largest (maximum) value in the distri-
bution;
3 the number that represents the middle value between the median and
the minimum value (we will refer to this value as the first quartile); and
4 the number that represents the middle value of the scores between the
median and the maximum value (we will refer to this value as the third
quartile).
The term hinge is also used to describe a value in the middle of each half of
the distribution defined by the median. Hinges are similar to quartiles. The
Examination Marks
95.0
85.0
75.0
65.0
55.0
45.0
35.0
40
30
20
10
0
FIGURE 5.2 Histogram of hypothetical examination marks
1
15

difference between hinges and quartiles is that hinges are defined in terms
of the median. They are often located closer to the median than quartiles.
The important features of most distributions of scores can be summarized
by five values: the minimum and maximum values, and the median and the
first and third quartiles. These five values are known as the five-number
summary. A boxplot is simply a visual representation of the five-number
summary (Velleman and Hoaglin, 1981).
The first step is to construct a `box' whose ends are defined by the first
and third quartiles. The length of the box is the difference in the values
of the quartiles. The second step is to draw a line within the box
represented by the median value. The third step is to draw lines outside
the box corresponding to the minimum and maximum values. These
lines are also known as whiskers. Sometimes the location of the whiskers
is defined differently. Some data analysts prefer to define the whiskers
of a boxplot in terms of the values that are 1.5 times the difference
between the quartiles. If there are scores beyond these modified whisker
values, then they are plotted individually. Figure 5.3 gives the anatomy of
a boxplot.
We can tell a great deal about a distribution of scores by examining its
corresponding boxplot. Consider two hypothetical variables X and Y. A
distribution of values for these variables is presented in Table 5.3.
By just `eye-balling' the data it appears that the values for X are more
skewed than the values for Y. The boxplots for the distribution of X and Y
are presented in Figure 5.4. Some features of these plots are noteworthy.
One observation is that the boxplot for X has only one whisker, an indica-
tion that the distribution is skewed. You will also see that the line represent-
ing the median is slightly `off-centre'. This is further evidence that the
distribution for X is skewed. On the other hand, you will notice that the
median for the distribution of Y is in the middle of the `box' component of
the boxplot, suggesting that the plot is not skewed.
Whiskers
Median
Quartile
Quartile
FIGURE 5.3 The anatomy of a boxplot
1
16

With a little experience, the data snooper can use boxplots to identify
particular features of a distribution. There are two key questions the data
snooper can ask when examining a boxplot. First, is one whisker longer
than the other whisker? If the answer is yes then this is an indication that
the distribution is skewed. With skewed distributions, the bar representing
the median will be off-centre. The second question one can ask when invest-
igating a boxplot is whether the `box' component of the plot is compressed
ng
10
10
N =
Y
X
10
8
6
4
2
0
1
FIGURE 5.4 Boxplots for two hypothetical variables Xand Y
TABLE 5.3 Hypothetical data for variables
Xand Y
Variable X VariableY
1.00 1.00
1.00 3.00
1.00 4.00
2.00 5.00
3.00 6.00
3.00 7.00
4.00 8.00
5.00 5.00
4.00 5.00
3.00 4.00
1
17

or elongated. The `box' component represents the spread of the middle half
of the distribution of values. If the `box' looks compressed, then the values
in the middle half of the distribution are `close together', falling within a
narrow range of values. Figure 5.5 shows these characteristics in two side-
by-side boxplots.
Boxplots are useful visual aids. But one should not rely solely on them for
understanding a set of data. In some cases, a boxplot can be misleading. For
instance, if the data you have just collected are bimodal (have two modes),
then a boxplot of those data will not indicate the presence of those modes.
In this case, a stem and leaf display would identify the bimodality of the
data, and provide the data analyst with a more accurate `picture' of the
data. Boxplots therefore should never be interpreted in isolation.
Tables, Graphs and Figures
`Getting information from a table is like extracting sunlight from a cucum-
ber.' Although this quote from Farquhar and Farquhar (1891) comes at the
turn of the 19th century, there are still instances in which the words ring
true in the 21st century.
Our knowledge about best practice with tables and graphs has improved
since Farquhar and Farquhar's day. Wainer (1992) found, from an analysis
of the use of tables and graphs to represent measurements, that they are
best used for three main purposes:
1 Tables and graphs can be used to identify and to extract single bits of
information; for example, what types of crimes were committed in
Sydney, Australia in 1999?
2 Tables and graphs can be used for trends, clusters or groupings; for
example, have the types of crimes in Sydney changed during 1995
to 1999?
Compressed distribution
Whiskers are different
lengths – skewed
distribution
Median off ce
- ntre
FIGURE 5.5 Side-by-side boxplots
1
18

3 Tables and graphs can be used to make group comparisons; for example,
we can ask the question, which crime is most frequent? Are the types of
crimes committed in Sydney different from those in London?
Tables and graphs represent a convenient and an effective way of summar-
izing information. A good table should enable the reader to understand at a
glance information that would be difficult to grasp if presented in the text.
A good table is simple and conveys information concisely.
The components of tables and graphs have also been the subject of study.
Sternberg (1977) said that a table has several key components:
1 Tables should be numbered. It is important to be able to identify a table
accurately when it is being discussed in the text,
2 Tables should be labelled appropriately and concisely. The title should
be unambiguous and understandable without reference to the text,
3 Tables usually contain columns. These columns should be clearly
labelled.
Sternberg identified four types of column headings. The first type of head-
ing is a stubhead. This column is typically located on the left of the table
and usually lists the independent variables in the study. The second type of
heading is called a boxhead; these are the headings at the top of a table.
Boxheads may cover more than one column. These subdivisions of a box-
head are referred to as column heads. The final type of heading that
Sternberg identified was a spanner head. Spanner heads cover the entire
body of a table. Some of these heading types are illustrated in the example
in Table 5.4, from Ho and Zemaitis (1981: 24).
The body of the table can contain both numerical and written content. In
the case of numerical content, the level of precision should be no more than
the data justify. Tables can also have footnotes. These should be informative
and concise.
Figures also enable the researcher to present information concisely.
Figures are useful because we can see at a glance conspicuous features
of the data. However, figures and graphs do have one important dis-
advantage ± they do not necessarily reveal precise values. Tables, on the
other hand, are precise and concise tools for conveying data and statistical
information (Sternberg, 1977).
Figures and graphs, like tables, should be titled. The title (also referred to
as the figure caption) should describe clearly and concisely what the graph
is reputed to demonstrate. The reader should be able to understand what
the figure or graph is about from the title without needing to refer to the
text. Figures should also be numbered. We usually use Arabic numbers to
refer to figures (Sternberg, 1977).
Finally, the text should not reproduce material presented in tables and
graphs. Obviously, it is important to discuss graphs and tables. They are,
after all, summaries (visual summaries in the case of graphs) of data and
1
19

information, and therefore need to be explained and elaborated in the text.
However, it is not good practice to replicate the content of a table or graph
in the text.
Does a Picture Always Paint a Thousand Words? Some issues with
representing data in graphical and tabular form
Although graphs and tables can be effective and efficient ways of conveying
and summarizing large amounts of information, there are occasions where
these tools can be used to mislead the inexperienced statistical sleuth.
One common trick used by researchers (and market researchers and
advertisers in particular) is manipulating the scale intervals on a graph in
order to exaggerate the result or finding. Let us assume that we have sur-
veyed the residents of a large Australian city to examine the preferred
telecommunications carrier. The researchers find that 53 per cent of respon-
dents preferred Carrier A while 47 per cent of respondents preferred Carrier
B. We can present these findings in a histogram as shown in Figure 5.6.
An inspection of this graph suggests that, although there is a difference
between preferences, this difference is small. Now consider the same data
presented in a somewhat different manner in Figure 5.7.
By changing the scale values in the vertical axis we have exaggerated the
difference between the preference for the two carriers. Note that in the
second figure we start the values on the vertical axis with 44, not 0 as is
the case in Figure 5.6. The experienced data snooper will check the values
on the scales depicted in graphs. As a rule of thumb, the scale values on the
vertical axis should begin with 0.
TABLE 5.4 The anatomy of a table (used by permission)
Table number
Table label
Table1 3
3
Number and proportion of male and female subjects who scored high and low on
the CONCOSS
Level of CONCOS
3
Proportion of High
Sex of subjects High
3
Low
3
CONCOS
Males 20 26 .43
Females 38 30 .55
Boxhead
Column head
120

The manipulation of information in a table or graph is not always
intended to mislead the reader. Abelson (1995) provides an example of
data manipulation or `reframing' (quite legitimately) that assists the articu-
lation of the results. Abelson cites a study by Beall (1994) that examines the
stereotype of women as more emotionally expressive than men. Abelson
notes that Beall presented male and female participants with a number of
vignettes. These vignettes depicted relatively simple social behaviours such
as touching someone's arm. Each vignette involved either a hypothetical
man or woman engaging in the behaviour. The behaviours were held
constant in these two versions. Each participant was asked to report the
intensity of the emotion using a seven-point scale. The data in Table 5.5
represent the mean intensity rating averaged over the vignette completed
by participants.
0
20
40
60
80
100
Carrier A Carrier B
percentage
FIGURE 5.6 Preference for telecommunications carrier
44
45
46
47
48
49
50
51
52
53
Carrier A Carrier B
percentage
FIGURE 5.7 A different way to display preference for telecommunications carrier
121

The means in this table tell us that female participants attribute more
emotional intensity to the behaviours than do males, but females do not
attribute more emotional intensity when the characters are male. As
Abelson notes, trying to understand the interaction between gender of the
participant and gender of the character is not straightforward in terms of
the original labelling of the columns in Table 5.5. A simple rearranging or
reframing of the data will assist in aiding the interpretation of the inter-
action. Table 5.6 presents the reframed data. Note that the columns now
represent the gender of the character relative to the subject ± is the gender of
the character either the same as or opposite to the gender of the participant?
Now the interpretation is more straightforward: Females attribute more
emotional intensity to characters that are of the same gender and opposite
gender than do males, but both males and females attribute more emotional
intensity to characters of their own gender (Abelson, 1995: 116). Reframing
the data has not tampered with its integrity. It has simply aided the reader
in understanding the point that the author wishes to make. It's a matter of
looking at the clues from a different angle or perspective.
USING SPSS AND EXCEL TO PLOT DATA:
Accounting for Tastes dataset
We will use a real dataset to show how SPSS and Excel, statistical and
spreadsheet software, can be used to plot and describe data. The SPSS
dataset, tastes.sav, has been taken by the authors from Bennett, Emmison
and Frow's comprehensive 1995 survey on the everyday culture of
Australians. The innovative survey is reported in Accounting for Tastes:
TABLE 5.5 Mean ratings of intensity of emotion
Gender of story character
Gender of subject Male Female
Male 4.52 4.20
Female 4.46 4.66
Column means 4.49 4.43
Source: Abelson,1995: 116
TABLE 5.6 Reframed data: mean ratings of intensity of emotion
Gender of story character
relative to participant
Gender of subject Male Female
Male 4.52 4.20
Female 4.66 4.46
Column means 4.59 4.33
Source: Abelson,1995
122

Australian Everyday Culture. Like our other case studies, it is an excellent
example of care taken in theory, the relationship between quantitative and
qualitative, operationalization and sampling.
Methodology and Operationalization
Bennett et al. (1999) wanted to find out about the relationship between
social class and culture. Do countries like Australia have a ruling class
that directly affects cultural choice (like going to the theatre, listening to
pop music)? Is there a `single powerful and universally binding scale of
cultural legitimacy which produces effects'? (1999: 269).
Accounting for Tastes is both a theoretical critique of Pierre Bourdieu's
ideas of social class and a presentation of their own ideas of `regimes of
value' (1999: 258±264). According to Bennett et al., regimes of value are
templates which structure cultural preferences. The templates might not
in all cases be explicitly set out: `but they are expressed and refined at
every level of cultural legislation, from literary and film criticism, to dis-
cussion at work about last night's television programs, to transient com-
ments about someone's good or bad taste in jewellery or in souped-up cars
or in colour schemes for the house' (1999: 259±260). Regimes of value can be
stable over time because they are grounded in administrative, economic,
technological, and legal infrastructures. `They are never simply expressive
of, and never simply reflect, a class structure, or the ethos of an age cohort
or a gender or a structure of sexual preference' (1999: 260).
To operationalize the Australian Everyday Cultures Project (AECP) class
model, Bennett and his colleagues collected information about their parti-
cipants' current occupation to determine their employment status as well as
managerial or supervisory status. Òn these initial filters we superimposed
a measure of the occupation's skill level based on the groups of the
Australian Standard Classification of Occupations (ASCO) devised by
the Australian Bureau of Statistics' (1999: 18). The resulting `class model'
consisted of nine categories: Never employed, employers, self-employed,
managers, professionals, para-professionals, supervisors, sales and clerical
workers, and manual workers.
`Cultural tastes' were defined by everything that the AECP could
conceive as `culture': ìncluding home-based leisure activities, fashion, the
ownership of cars and electronic equipment, eating habits, friendships,
holidays, outdoor activities, gambling, sport, reading, artistic pursuits,
watching television, cinema-going, and the use of libraries, museums and
art galleries' (1999: 2).
The sampling frame for the AECP survey was based on the August 1994
Australian Electoral Roll. À total of 5000 non-institutionalized adults were
obtained by firstly stratifying by state and territory and then applying
systematic random sampling within these strata' (1999: 270). Of 5,000
questionnaires a total of 500 were returned undelivered; 450 were returned
123

as refusals, with a total of 2,756 usable returns, making a response rate of
61.9 per cent. Table 5.7 shows the stratified sample and the official statistics.
Bennett et al. (1999) also conducted a major pilot in Brisbane and
associated areas before conducting the survey. This included extensive
qualitative focus groups in order to explore frame of reference. Data from
these groups are represented in the study, providing an ethnographic
component to the study. Bennett and his colleagues acknowledged the
limitations that definition of constructs may place on their findings:
The categories that organise our survey are constructs, artifices of method which
frames the questions in a certain way, chooses a particular form of the indepen-
dent variables, weights the data to conform to the national census figures, and
subjects them to complex statistical manipulations (each with its inbuilt assump-
tions) to produce the `findings' which then form the raw material for theoretical
interpretation. (1999: 15)
While Accounting for Tastes had theoretical reservations regarding quantita-
tive survey methods, it argued that these problems related mainly to how
the results of such methods are presented, rather than the unsuitability of
quantitative methods per se. `We said earlier that our interest in such
methods was prompted partly by a wish to subject cultural studies to a
disciplined form of engagement with ``the real''. The danger, though, is that
if interpreted in the light of the positivist assumptions which often accom-
pany them, the results of quantitative methodologies can often be mistaken
for reality itself' (1999: 15). Here we have echoes of both Hoftstede and
Lazarsfeld.
Working with SPSS
The dataset for Accounting for Tastes is available through the Australian
National University Social Sciences Data Archive (http://ssda.anu.
edu.au/). The description below, provided through the archive, provides
TABLE 5.7 Accounting for tastes: comparison of stratified sample with official stastistics
1995 Everyday 1994 Australian Bureau of Statistics
Australian State/Territory Culture Survey estimates
NorthernTerritory (19) 0.7 1.0
Australian Capital Territory (51) 1.9 1.7
Tasmania (72) 2.6 2.6
Western Australia (246) 8.9 9.6
South Australia (253) 9.2 8.2
Queensland (529) 19.2 18.0
New SouthWales (867) 31.5 33.9
Victoria (719) 26.1 25.0
N ˆ 2,756 100.0 100.0
124

an overview of the dataset and the study itself. Many scholars send their
datasets to data archives in order to provide other researchers with access to
the raw data. There is normally a small fee for ordering the dataset and
specific permissions required for using those datasets.
Social Science Data Archives
The Australian National University
Research Topic (Abstract)
The Australian Everyday Consumption project represents the first ever study of
Australians' cultural consumption. The study aims to delineate the cultural activ-
ities of Australians and their relationship to social class. The survey covers a broad
range of cultural pursuits, and variables include the books, newspapers and
magazines people read; the film and television programs they watch; the types
of cars they drive and possession of other consumer durables; their musical inter-
ests; the suburbs they live in; their homes and levels of home ownership; whether
they gamble; their hobbies; whether they play and/or watch sport; membership of
clubs; what they eat; their pets; how often they attend galleries, concerts and/or
the theatre; the clothes they wear; their families and friends; working conditions
and working hours; comparisons with spouse and parents; personal and house-
hold financial details; religious beliefs and practices; and their attitudes towards
societal classes, culture, politics and government, finance and the economy, trade
unions, gender and employment, and Aboriginal land rights. Background vari-
ables include respondents age, sex, marital status, level of education, country of
birth, work status, income and occupation.
Subject Terms
Accommodation; Arts; Assimilation (cultural); Attitudes; Broadcasting; Careers;
Clothing; Clubs; Community involvement; Diet; Education; Employment; Ethnic
groups; Family; Films; Food; Gambling; Human relations; Income; Leisure; Living
standards; Mass media; Motor cars; Music; Newspapers; Performing arts; Politics;
Radio; Radio programmes; Reading; Religion; Social classes; Social responsibility;
Sports; Television; Television programmes; Travel; Values; Working conditions;
Working hours.
Kind of Data
Survey
Time Dimensions
cross-sectional (one-time) study
Definition of Total Universe (Universe Sampled)
All non-institutionalised Australian adults, aged 18 years and over who were on
the July 1994 Commonwealth Electoral Roll.
Sampling Procedures
Stratified random sample
Number of Units (Cases)
number of units in original sample: 5,000
number of losses: 2,244
number of replacements: 0
number of cases (unweighted): 2,756
125

Dates of Data Collection
first date of data collection: November 1994
last date of data collection: March 1995
Method of Data Collection
self-completion (mail out, mail back)
Dimensions of Dataset
number of cases: 2,756.
number of variables per case: 633
Accessibility
A copy of the User Undertaking Form must be signed before data may be
accessed.
The datafile tastes.sav is in SPSS format. SPSS is one of the most com-
monly used statistical packages in the social sciences. We will use Version
9.0 of SPSS to show how histograms, stem and leaf displays and boxplots
are obtained from SPSS. The Statistical Inquirer, multimedia courseware pro-
vided with this text, provides introductory lessons in descriptive statistics.
The courseware also provides brief, dynamic, exercises on the functions of
SPSS. The exercises use a real dataset from the doctoral work of Patrick
Rawstorne at the University of Wollongong. This dataset is available as an
SPSS file for practice in SPSS.
Once you have opened a data file in SPSS, such as the Accounting for
Tastes tastes.sav file that we are using here, the data editor in SPSS will
look like this.
op
126

Let's consider the variable `housinc', annual household income. We may
be interested in exploring the distribution of annual household incomes. In
this chapter we have looked at histograms, stem and leaf displays and
boxplots as ways of representing data visually. There are a number of
ways of using SPSS to construct these plots. One way is to use the Explore
option. Select Descriptive Statistics from the Analyze menu. Choose the
Explore option from Descriptive Statistics.
Once you have selected Explore, the following dialog box will appear.
Select the variable you wish to analyse, in this case `housinc', and move it
to the Dependent List window by clicking on the uppermost arrow button.
Select the Plots display button located in the lower left-hand corner of the
dialog box.
The next step is to select the types of plots you wish to construct. This is
done by clicking on the Plots button located on the lower right-hand corner
of the window. [Note that you also have the option of comparing boxplots.
You could, for example, include a grouping variable in the Factor List win-
r
127

dow. This would allow you to draw boxplots for each level of the grouping
variable, such as gender.] The following window should appear.
Ensure that the Histogram option is checked. The boxplot and stem and leaf
display options are default selections. Then click Continue and OK. This will
generate the output.
Here is the stem and leaf display output associated with the same data.
Frequency Stem Leaf
106.00 0 . 00000000000013
106.00 0 . 555777777777777
190.00 1 . 000000000000333333333333333
174.00 1 . 6666666666666666999999999
162.00 2 . 11111111111133333333333
286.00 2 . 55555555555555999999999999999999999999999
.00 3 .
216.00 3 . 6666666666666666666666666666666
.00 4 .
265.00 4 . 55555555555555555555555555555555555555
.00 5 .
222.00 5 . 55555555555555555555555555555555
.00 6 .
192.00 6 . 555555555555555555555555555
.00 7 .
134.00 7 . 5555555555555555555
.00 8 .
62.00 8 . 555555555
.00 9 .
57.00 9 . 55555555
111.00 Extremes (ˆ 110000)
Stem width: 10000.00
Each leaf: 7 case(s)
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The boxplot output summarizes the distribution:
We can see from these displays that the data on household income are
slightly skewed. The histogram and stem and leaf representations are
asymmetrical; most of the values are between $10,000 and $45,000. From
the boxplot display we see that the whiskers are of different lengths and the
median is just slightly off-centre ± clues that the data may be skewed. The
boxplot display also indicates the presence of possible extreme values
(annual household incomes of $110,000).
Histograms and boxplots can also be constructed by selecting Histogram
or Boxplot from the Graphs menu.
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If you select the Boxplot option, the following dialog box appears.
Ensure that you have selected Summaries of separate variables by clicking on
it. Click on Define to obtain the next dialog box.
We will select the variable `housinc', labelled annual household income,
and move it to the Boxes Represent window by clicking on the arrow button.
Click on OK to generate the output.
If you select Histogram from the Graphs option you will see the following
dialog box.
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Select the variable from the variable list and move it to the Variable window
by clicking on the arrow button. Click on OK to generate the histogram.
Working with Excel
There are alternative software packages that enable you to create histo-
grams, stem and leaf displays and boxplots. Microsoft's Windows 97
version of Excel is not a statistical package. None the less, it provides a
number of very useful data manipulation and data analytic tools. Excel does
not provide a menu option that will allow you to construct stem and leaf
displays or boxplots. However, it is possible to write macros in Excel that
would allow you to construct these plots.
There are a number of ways to construct a histogram using Excel. One
way is to make use of the data analysis tools available in the Analysis
ToolPak. The data analysis procedures are available from the Tools menu.
The following example uses the `housinc' variable from the tastes.sav
data file.
From this menu you can select the Data Analysis option and access
the following dialog box. The Data Analysis dialog box lists a number of
statistical procedures, including the option for constructing a histogram.
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Select Histogram and click OK. You should now have the next dialog box.
In this box we include the cell range that includes the data we wish
to analyse. You select this range by simply clicking on the first cell
(not the cell containing the variable label) of the column containing the
data and then clicking on the last cell. Click OK. This procedure will
generate a frequency distribution on a separate Excel worksheet. You
can then use the chart wizard to construct a graph of this frequency
distribution.
DESCRIBING DATA
Numerical Summaries: What are they and why are they important?
We have looked at ways of graphically representing a set of numerical
values for a particular variable. We can use these techniques to compare
sets of values or distributions. However, there is a problem associated with
using some graphical techniques to compare distributions. The problem is
related to the fact that plots such as stem and leaf displays represent all the
data at an individual level. It is important to be able to summarize the main
features or properties of a distribution of scores. The experienced data
snooper responds to the request `Give me the facts' not by taking short
cuts but by summarizing the facts in a meaningful way and without sub-
stantial loss of information.
Most distributions have three important features, namely, the shape of
the distribution, the location or central tendency of the distribution and
the spread of scores in that distribution. For a particular distribution
it is possible to derive measures or indices for these distributional
characteristics.
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Describing Location or Centrality
Some Notation
To assist us in defining some indices of location and spread, it is useful to
use some mathematical notation. Any kind of mathematical notation is
enough to send some people into fits of panic. For those of you who are
`notation phobic', remember that mathematics is just another language that
we can learn ± admittedly a very specialized language, but parts of it are
easy to learn. The game is afoot!!
Assume we are measuring a variable ± the number of standard drinks
consumed by Australian men aged between 20 and 21. For illustrative
purposes let us also assume that we have data for five men. The
values are 3 5 2 4 4 respectively. We can use the letter X to represent the
variable of interest, in this case, number of standard drinks consumed by
Australian men aged between 20 and 21. In this example, the variable takes
on five values. Let the individual values be represented by x1, x2, x3, x4, and
x5 respectively. The subscript identifies a particular individual. That is, x1
represents the value for person 1 (the value 3), x2 represents the value for
person 2 (the value 5), and so on. If we had n individuals then the nth value
for the variable X would be represented as xn, and the value for the ith
individual would be represented by xi:
In defining some numerical summaries we want to add up or sum values.
The operation of summing values is abbreviated or represented by , the
Greek letter upper-case sigma. The operation of summing n values, x1,
x2,. . .,xn, that is x1 ‡ x2 ‡ . . . ‡ xn, can be represented as xi.
The most used and familiar measure of centrality is the arithmetic
mean or average. Computing the mean is quite simple. You simply
add up the values and divide by the number of values that you have.
If we have n values, x1,x2,. . .,xn, then the mean, M, is represented
algebraically as:
M ˆ x1 ‡ x2 ‡ . . . ‡ xn†=n
Another important measure of centrality is the median. We introduced this
index when we discussed boxplots earlier. You will recall that the median is
defined as the point at or below which 50 per cent of the values fall. If we
were to rank-order our data from lowest to highest values, then the median
is the middle value in the rank order. Therefore, the median may be thought
of as the `typical' value in a set of data.
Assuming we have n values, we can use the formula n ‡ 1†=2 to
calculate the rank position of the median. If we have an odd number of
values, this formula will give an integer value for the rank position.
However, if we have an even number of values, the rank will not be integer.
In this case we define the median as the rank of the two middle values in
the distribution.
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Example 5.2: Calculating the median of odd and even numbered
distributions
The following numbers are measures of diastolic blood pressure obtained from five
men in an experiment on reactions to the movie The Hound of the Baskervilles:
72 88 90 84 86
To calculate the median we first rank-order the scores:
72 84 86 88 90
Using formula n ‡ 1†=2 we find that the rank position of the median is
5 ‡ 1†=2 ˆ 3.The third value in the set of values is 86.
We also obtain the diastolic blood pressure for a sixth man, with a value of100.
Then the rank position of the median is 6 ‡ 1†=2 ˆ 3:5. The median lies between
the third and fourth values of our ordered set, namely 86 and 88.The median in this
case is the average of these two values, namely 86 ‡ 88†=2 ˆ 87. Note that the
value of the median is not actually in our set of values.
A median can be found for data that are usually interval in nature, although
you could find the median ordinal data. However, we generally do not
calculate the median for categorical or nominal-level data since these classes
of measurement are not ordered.
A third measure of central tendency is the mode. It is probably the most
obvious measure of location. The mode is simply the most frequently occur-
ring value in a distribution. This definition allows for the possibility of more
than one mode for a distribution. This is one reason why the mode is not
particularly useful as a measure of centrality and therefore not generally
reported.
Mean vs. Median (When is the evidence not contaminated?)
Although both are measures of centrality the mean and median do not
measure the same thing. Consider the following scenario. You are asked
by a close and dear friend to help him purchase a home. He is returning to
your suburb after working interstate for a number of years. Being a good
friend you decide to help him out by inquiring about home prices in your
suburb. You visit the local professor in real estate, Professor Moriarty, and
are told that the average home prices in your area have risen from $200,000
to $300,000 in the past two years. This seems like excellent news for your
friend. Or is it? Is the average home price the best indicator of values in
your area? Or is this statistic `contaminated'?
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The mean or average is not always the best indicator of the `typical' value
in a set of data. Consider the following home prices in a quiet cul-de-sac:
$150; 000 $160; 000 $170; 000 $170; 000 $180; 000
The average of these values is $166,000; the median value is $170,000. Now
let us assume that the home valued at $150,000 is sold, demolished and a
new home built in its place, valued at $300,000. What effect does this have
on the mean and median values? The median value is still $170,000 but the
mean value has rise to $196,000! Does the mean still represent the typical
home price in the street? You can see that having an atypical or extreme
value in a set of data affects the mean value. In fact you can make the mean
as large as you like simply by increasing the value of just one value in the
batch! On the other hand, the median is unaffected by or resistant to these
extreme values. That is, the median is a resistant measure.
Will you ask Professor Moriarty for more clues? What would the good
data snooper ask for?
Describing Variability
An important characteristic of a set or distribution of values is the way
those values vary from each other, the spread or variability of the distri-
bution. At times it is more important to consider how scores vary than to
describe the typical value in a distribution of scores. For example, the med-
ian annual incomes of two groups of individuals may be the same, but, for
one group, the distribution of scores may have some extreme values, indi-
cating extremes in relative incomes (and wealth, if wealth is operationalized
as annual income!).
One way to describe the variability of scores in a distribution is to plot
those scores. But are there summary measures or indices of variability that
we can use?
A very simple measure of spread is the range. The range is defined as the
difference between the largest and smallest values in the distribution.
Consider two sets of scores:
Set 1: 2 6 7 8 10 11
Set 2: 1 1 1 2 3 3
The range for Set 1 is 11 2 ˆ 9, while the range for Set 2 is 3 1 ˆ 2. You
can see that Set 1 has a larger range than Set 2, indicating that the spread of
scores is greater for Set 1 than Set 2. However, the range is not a resistant
measure of spread. Let's say Set 2 consisted of the following values:
Set 2: 1 1 1 2 3 10
The range is now is 10 1 ˆ 9, the same as for Set 1. But the spread of
scores for each distribution is quite different!
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We can describe the spread of a distribution in terms of percentiles. A
percentile corresponds to a value in a distribution such that a certain percent-
age of the distribution falls above or below it. The median, for example, is
the 50th percentile, since 50 per cent of the values in a distribution fall above
the median, and 50 per cent fall below it.
We defined two other important percentiles when we discussed boxplots.
Quartiles are percentiles; the first quartile (abbreviated Q1) is the 25th per-
centile, and the third quartile Q3† is the 75th percentile. The quartiles are
quite simple to calculate. We first need to rank-order our observations. We
then locate the median. The first quartile is the median of those observa-
tions that lie below the median. The third quartile is the median of those
values above the median. Imagine a piece of paper representing the set of
observations. If you fold the paper into two equal halves, the fold represents
the median. If you fold the paper again so that you have four equal quar-
ters, the first and third fold marks represent the first and third quartiles.
A very simple and useful measure of spread is the distance between the
quartiles. This measure is known as the interquartile range (IQR).
Symbolically,
IQR ˆ Q3 Q1
You will recall that it corresponds to the edges of the `box' in a boxplot. An
important feature of the quartiles and the IQR is that they are resistant
measures.
The IQR can also be used to identify extreme values in a set of
observations. One commonly used rule is to define extreme values or
outliers as those values that lie at least 1.5 times the value of the IQR
1:5 IQR† below the first quartile or above the third quartile.
Perhaps the most commonly used measure of spread is the variance (and
the associated measure of standard deviation). These measures are defined
in terms of variation about the mean as the measure of location. These
measures, therefore, are not resistant, yet they are extremely common in
social science research.
Third quartile
First quartile
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The logic behind variance as a measure of spread goes as follows: Let's
define the mean M† as the measure of centrality of a set of n observations
xi†. Each observation deviates from the mean by a certain amount xi M†.
Now one possible measure of spread would be to add up all possible devi-
ations. However, some observations will lie below the mean, and therefore,
xi M will be negative; some observations will fall above the mean and
xi M will be positive. In fact the sum of these deviations, xi M, will
always be 0. A way around this problem is to square the deviations before
summing them. The variance is computed by taking the sum of squared
deviations and dividing this sum by n 1. The variance can be interpreted
as an average squared deviation. We will use the symbol s2
to represent the
variance. Algebraically, s2
is:
s2
ˆ 1= n 1†‰ x1 M†2
‡ x2 M†2
‡ . . . ‡ xn M†2
Š
The variance has one disadvantage as a measure of spread. Let's say you are
measuring weight in kg, then the variance will be measured in squared kg,
since we are computing squared deviations. To return the variance to the
same units of measurement as the original values, we take the square root of
the variance. We call this new index the standard deviation, represented
symbolically as s.
Example 5.3: Calculating the variance of a set of values
Famous psychologist Prof. Loshonski has constructed a new measure to assess the
degree to which people are susceptible to deception.The measure generates a score
ranging from1to 20, where1means `not susceptible at all'and 20 means `extremely
susceptible'. Prof. Loshonski obtains scores from five people.Their scores are 4, 6, 8,
10,12, respectively.To calculate the variance of these scores we begin by computing
the mean.
M ˆ 4 ‡ 6 ‡ 8 ‡ 10 ‡ 12†=5 ˆ 40=5 ˆ 8
Next we calculate the deviation scores, square them and sum up.These computations
are presented in the following table:
ÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐÐ
xi xi M xi M†2
4 4 8 ˆ 4 4†2
ˆ 16
6 6 8 ˆ 2 2†2
ˆ 4
8 8 8 ˆ 0 0†2
ˆ 0
10 10 8 ˆ 2 2†2
ˆ 4
12 12 8 ˆ 4 4†2
ˆ 16
xi M† ˆ 0 xi M†2
ˆ 40
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s2
ˆ 1= n 1†‰ x1 M†2
‡ x2 M†2
‡ . . . ‡ xn M†2
Š
ˆ 1= n 1†‰16 ‡ 4 ‡ 0 ‡ 4 ‡ 16Š
ˆ 1= 5 1†‰40Š
ˆ 40=10
ˆ 10
The variance of the five scores is10. The standard deviation is the square root of10
which is 3.16.
We have already noted that the standard deviation is not a resistant meas-
ure of spread. If the distribution is skewed, the standard deviation will not
be a good measure of spread. So why use it? One reason is that the standard
deviation plays an important role in mathematical statistics, in particular in
its role in the normal distribution. We will examine this role in the next
chapter. But for now it is important to note that the good statistical sleuth
will be cautious about interpreting indices in isolation. You need to look at
all the facts, not just one bit of evidence. You cannot interpret an index or
measure like the standard deviation without asking `Show me the data!!
Show the me data!!'. Indices such as the standard deviation need to be
interpreted in the context of the distribution they are based on.
USING SPSS AND EXCEL TO DESCRIBE DATA
Working with SPSS
The Explore option in SPSS allows the researcher to construct histograms,
stem and leaf displays and boxplots for a set of values. This option, how-
ever, can also be used to generate all of the descriptive statistics we have
discussed in this chapter. Let's consider again the variable `housinc' for the
tastes.sav data file.
Recall that we access the Explore option by going to the Analyze menu and
then selecting Descriptive Statistics. The following dialog box should appear.
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Select the variable of interest, in this case `housinc', and move it to the
Dependent List. Select Statistics from the Display option located in the
lower left-hand corner of the dialog box. Clicking on the Statistics button
located in the lower right-hand corner of the dialog box will bring up the
next dialog box.
The default option should have the Descriptives option selected. Note that
you can also select Percentiles to generate values corresponding to each
percentile. Click Continue and then click OK. You should then have the
following output.
Descriptives
Statistic Std.Error
annual household Mean 41577.53 587.2969
income 95% Confidence Lower Bound 40425.84
Interval for Mean Upper Bound 42729.22
5% Trimmed Mean 40069.84
Median 36000.00
Variance 7.9E‡ 08
Std.Deviation 28061.49
Minimum .00
Maximum 110000.0
Range 110000.0
Interquartile Range 36000.00
Skewness 0.716 0.051
Kurtosis 0.134 0.102
This output contains both measures of centrality and the dispersion.
We can also compute descriptive statistics using the Descriptives option
from Descriptive Statistics in the Analyze menu.
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Once the Descriptives option has been selected, a dialog box will allow the
researcher to select the variable of interest in the usual way. It is possible to
control the type of descriptive statistic that is computed by clicking on the
Options button (located in the lower right-hand corner of the dialog box).
Note that the median and interquartile range are not selections in this
option. Click on Continue and then OK to carry out the procedure.
Working with Excel
There are various ways of generating descriptive statistics in Excel.
We will confine our discussion to using the Data Analysis option in the
Tools menu.
140

Once we have selected Data Analysis, we can select the Descriptive Statistics
option. The following dialog box will appear.
Define in the Input Range window the cell range covering the data values
you wish to analyse. The values for the variables of interest are in column K.
They start in row 2 and end in row 2757. To define these values in the Input
Range window, you first click on the first data point in column K (this is cell
$K$2, that is, the second row in column K). You then type a colon : and click
on the cell containing the last data value (this will be cell $K$2757, the
2757th row in column K). Select the option Summary statistics, and click
OK. This procedure should generate the following output in a separate
Excel worksheet.
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Both Excel and SPSS can be used to describe data. When new versions of the
statistical packages come out there are sometimes changes to the menu tabs
and the step-by-step dialog box procedures for deriving those descriptions.
However, as long as you are aware of the basic processes for deriving
graphical displays, such as summary statistics, you should not have diffi-
culty adapting to any new versions of the software.
Excel is a spreadsheet with built-in statistical and graphing tools. SPSS is
a powerful and comprehensive stand-alone statistical package. We saw, for
example, that Excel does not readily produce stem and leaf displays or
boxplots, although it is possible to write macros to produce these plots.
Excel has benefits because it is part of the widely used Microsoft Office
suite, making it more accessible to most people with computers.
SUMMARY
Observation does not stop suddenly when the social scientist has defined
the variables and collected the statistics. The processes of reasoning about
observations ± induction, deduction and abduction ± continue after the data
have been collected. Numbers require analysis and interpretation.
The good statistical sleuth has a number of tools and strategies to assist
him or her in the organization and understanding of data. The experienced
data snooper explores the data, obtaining summary statistics that give an
overview of what is happening. The data snooper can use a table or a figure
to highlight important features, including the incongruous, the unexpected
and the peculiar. Graphs and figures, however, have limitations ± they can
be used to exaggerate findings as well as to clarify them. Tabular and visual
displays are important in presenting findings and the corresponding
142

arguments, but the good data snooper always asks for the data and checks
the validity of the claims being made.
The data from a study normally go into a variable by case matrix ± a
dataset. The Accounting for Tastes project has a relatively large dataset. We
can describe the main characteristics of that dataset in terms of its shape, the
location or centrality of the data and the dispersion or spread of the data.
We discussed a number of summary measures or indices of centrality and
dispersion. Measures of centrality provide information about what is typ-
ical or average. They are important and useful statistical information. But
care needs to be taken when interpreting and discussing measures of cen-
trality. These measures are summary indices and we can lose information
on the individual datum ± the individual case.
We also considered several measures of variability or dispersion.
Measures of centrality provide the statistical sleuth with clues about
where most of the data are centred or located. These measures, though,
do not provide the sleuth with any information on the variability of the
data. A more complete set of clues on a dataset would include an appro-
priate measure of dispersion. As with measures of centrality, there is no
single `best' measure of variability. The statistical sleuth must choose
between dispersion indices and select a measure that is appropriate for
the situation.
Understanding the language of statistics ± the notation and formulae ± is
important for making informed decisions about the choice of statistical
measures. Each of the measures has a role in understanding the nature of
the data and its limitations. We also need to remember that statistical
packages are not substitutes for a sound working knowledge of the data
analysis procedures. The experienced statistical sleuth will know that cer-
tain techniques and measures are appropriate and meaningful for a par-
ticular dataset, and then use a spreadsheet or statistical package to carry out
the analysis or generate the graphs. Statistical knowledge is indispensable
when interpreting output generated by a package. The statistical package
will not interpret the output for us ± Elementary!
We provide brief lessons on SPSS in the The Statistical Inquirer CD-ROM,
as well as access to an SPSS data file computer anxiety.sav from a study on
computer anxiety. Use these lessons and the lessons on descriptive statistics
to broaden your knowledge about basic statistical procedures. In Chapter 6,
we will continue our exploration of SPSS and Excel as valuable (some
would say essential) tools in data analysis.
MAIN POINTS
. Numbers are not neutral. They form patterns and tell a story.
. Good statistical detective work involves making sense of the data col-
lected. We begin our statistical detective work by exploring data.
143

. Plotting data is a good way of exploring data. There are many ways of
representing data visually. Three commonly used methods are stem and
leaf displays, boxplots and histograms. We can use these methods to
compare distributions and identify salient features of distributions.
. Tables can be used to organize and present information. Tables and
graphs should be labelled appropriately and numbered consecutively.
. Large amounts of data can be summarized to account for centrality and
variability.
. The mean, mode and median are measures of central tendency or cen-
trality. The median is said to be a resistant statistic because the size of the
median is unaffected by extreme values in the distribution.
. The range, standard deviation, variance and interquartile range are
measures of dispersion or variability.
REVIEW EXERCISES
1 Statistics students at a regional university complete a confidential
survey about each lecturer, indicating to what extent they find the
lecturer a likeable person, on a scale from 0 to 7 where 0 means `not
likeable' and 7 means `very likeable'. Data are collected for 20
lecturers and presented below:
6 3 3 4 3 5 5 6 3 5 2 6 5 5 3 7 5 4 7 2
Construct a stem and leaf display for these data. Comment on the
distribution of popularity ratings.
2 Popularity ratings for psychology lecturers are obtained from
students at the same regional university as in Question 1.
Students rated 20 psychology lecturers on a popularity scale from
0 to 7 where 0 means `not likeable' and 7 means `very likeable'. Data
are collected for 20 lecturers and presented below:
4 6 7 4 3 6 4 6 3 5 3 6 5 5 4 7 5 6 7 3
Compute the five-number summary and draw a boxplot for these
data. Draw a boxplot for the popularity ratings of statistics lecturers
and compare this plot with the plot for psychology students. What
conclusions can you arrive at by comparing the boxplots for
statistics and psychology lecturers?
3 A psychologist examines the effects of environmental noise on
mental performance. She randomly selects two groups of students.
One group, Group 1, is given a problem-solving task while loud
environmental noise is played in the background. The second
group, Group 2, completes the same problem-solving task under
144

quiet conditions. High scores indicate good performance. The
scores for the two groups are as follows:
Group 1: 18 20 22 21 15 17 20 26 21
Group 2: 23 23 22 27 22 23 20 20 27
Compute the mean, median and mode for each group. Compare the
standard deviations for each group. What can you conclude?
4 Here's an exercise worthy of Sherlock Holmes, famous detective
and amateur statistician. Choose any four numbers from 1 to 10;
you can repeat a number if you wish. How many ways are there of
choosing any four numbers so that the variance of those numbers is
as small as possible? How many ways are there of choosing any
four numbers so that the variance of those numbers is as large as
possible? Does the situation change if repeat numbers are not
allowed? (Adapted from Moore and McCabe, 1993: 55.)
5 The sociology department of an Australian university, seeing its
staff as solid golfers, decides to enter its staff members in an annual
`Socio-Golf' tournament, an intervarsity tournament. The golf
scores of the 15 staff members are:
88 80 85 92 86 88 90 100 103 105 77 76 81 80 75
Compute the standard deviation and interquartile range for these
data. Based on the shape of the distribution, what measure of
dispersion would you report and why?
6 Derive summary statistics from the dataset computeranxiety.sav on
The Statistical Inquirer CD-ROM. The SPSS lessons on the CD-ROM
will give you clues on how to derive summary statistics from the
dataset.
REFERENCES
Abelson, R.P. (1995) Statistics as Principled Argument. Hillsdale: Lawrence Erlbaum
Associates.
Beall, A. (1994) Gender and the perception of evolution. Unpublished doctoral dis-
sertation, Yale University, New Haven, CT.
Bennett, T., Emmison, M. and Frow, J. (1999) Accounting for Tastes: Australian
Everyday Culture. Cambridge: Cambridge University Press.
Chambers, J.M. et al. (1983) Graphical Methods for Data Analysis. Belmont, CA:
Duxbury Press.
Christie, A. (1982) Poirot Loses a Client. New York: Dell.
Doubleday.
Farquhar, A.B. and Farquhar, H. (1891) Economic and Industrial Delusions: A discourse
of the case for protection. New York: Putnam.
145

Hansel, C.E.M. (1980) ESP and Parapsychology: A critical re-evaluation. Buffalo, NY:
Prometheus Books.
Ho, R. and Zemaitis, R. (1981) `Concern over the negative consequences of success',
Australian Journal of Psychology, 33: 19±28.
Rawstorne, P.R., Caputi, P. and Smith, B. (1998) `Toward the development of a meas-
ure of subjective computer experience'. Unpublished Manuscript, University of
Wollongong, Australia.
Rhine, J.B. and Pratt, J.G. (1954) `A review of the Pearce-Pratt Distance Series of ESP
tests', Journal of Parapsychology, 18: 165±77.
Sternberg, R.J. (1977) Writing the Psychology Paper. Woodbury, NY: Barron's
Educational Series.
Tukey, J.W. (1977) Exploratory Data Analysis. Reading, MA: Addison-Wesley.
Velleman, P.F. and Hoaglin, D.C. (1981) Applications, Basics and Computing of
Exploratory Data Analysis. Duxbury Press, Boston.
Wainer, H. (1992) Understanding Graphs and Tables. Technical Report No. 92-19.
Princeton New Jersey: Educational Testing Service.
146

6
Finding Answers from the Inquiry
Èlementary, my dear Watson!'
Sherlock Holmes had two purposes in mind when he used the word èle-
mentary'. The first purpose was to demonstrate the brilliance and simplicity
of his solution to a problem. The second was to show Dr Watson that the
conclusion had to follow from the evidence. Careful collection of evidence
and creative insight mark Holmes as the stereotype of the brilliant problem-
solver.
The solution to one problem in a crime case, of course, is not necessarily a
solution to the whole case. In his cases, Holmes goes through all the stages
of research: exploration, collection of data, analysis and findings. The accu-
mulation of clues assists in solving the case, but it is the relationships
between those clues that matter most. As the evidence builds up and the
detective builds the links between his or her observations, a picture
emerges. At a certain point, the detective starts to reconstruct what hap-
pened. Ellery Queen, the detective in The Dutch Shoe Mystery, reconstructs
from his observations what he thought to be the murderer's actions.
10:29 The real Dr Janney called away.
10:30 Lucille Price opens door from Anteroom, slips into Anteroom lift, closes
door, fastens East Corridor door to prevent interruptions, dons shoes, white
duck trousers, gown, cap and gag previously planted there or somewhere in
the Anteroom, leaves her own shoes in elevator, her own clothes being
covered by the new. Slips into East Corridor via lift door, turns corner
into South Corridor, goes along South Corridor until she reaches
Anaesthesia Room. Limping all the time, in imitation of Janney, with gag
concealing her features and cap her hair, she passes rapidly through the
Anaesthesia Room, being seen by Dr Byers, Miss Obermann and Cudahy,
and enters Anteroom, closing door behind her.
10:34 Approaches comatose Mrs. Doorn, strangles her with wire concealed under
her clothes; calls out in her own voice at appropriate time, Ì'll be out in a
moment, Dr Janney!' or words to that effect. (Of course, she did not go into
the Sterilizing Room as she claimed in her testimony.) When Dr Gold stuck
his head into the Anteroom he saw Miss Price in surgical robes bending
over the body, her back to him. Naturally Gold did not see a nurse; there
was none, as such, there.
10:38 Leaves Anteroom through Anaethesia Room, retraces steps along South and
East Corridors, slips into lift, removes male garments, puts on own shoes,
hurries out again to deposit male clothes in telephone booth just outside lift
door, and returns to Anteroom via lift door as before.

10:43 Is back in Anteroom in her own personality as Lucille Price. (Queen, 1983:
234±5)
`The entire process consumed no more than twelve minutes', says Queen.
Ellery Queen is right. Lucille Price killed Mrs Doorn, the hospital's
benefactor. But there is more to the story. Why did Price kill Doorn? And
was anyone else involved? Each step in the problem-solving process leads
to other steps. The detective has to decide not only which observations
count as clues, but also which relationships between clues are useful and
meaningful. We have already raised some of these issues in the discussion
on validity in Chapter 4.
The social scientist can learn from the idea of the detective as the data
collector and creative problem-solver, as Innes (1965) points out in his
critique of Sherlock Holmes. `Before any solution can appear the subject
must perceive that a problem exists' (1965: 12). Holmes, like Ellery
Queen, is sensitive to deficiencies in evidence and he is able to identify
`gaps' in the evidence. Holmes is motivated by curiosity in the unique
and novel, `the incongruous' (1965: 14). This ability relies on more than
`rational' and `deductive' processes. It also relies on emotive and evaluative
processes that associate previously unrelated ideas. The creative genius
Isaac Newton, Innes notes, also engaged in detective work (1965: 15).
Linking ideas together is a creative act, but empirical evidence ± observa-
tions ± assist in this process. Holmes was systematic in his collection and
recording of information for future reference. He had a card index of crim-
inals and news items.
At all times he practises his ability to notice fine details and to make judgements
as to the character of his client and of the criminal on the basis of his previous
knowledge. An example will make this clearer. In the tale of the Red-Headed League
Holmes makes the following observation.
`Beyond the obvious facts that he has at some time done manual labour, that he
takes snuff, that he is a Freemason, that he has been in China, and that he has
done a considerable amount of writing lately, I can deduce nothing else.'
After being asked the obvious question by his prompt, Dr Watson, Holmes goes
on to observe that the man's right hand is a size larger than his left, that he wears a
breast pin of an arc and compass, that his right sleeve is very shiny for five inches
and the left has a smooth patch where it has rested on the desk, and finally that on
his right wrist he has a tattoo mark stained in a manner only practised in China.
This last point is important, as Holmes is able to make this comment because he
has contributed to the literature on tattoo marks. Had it not been for this expert
knowledge then he could have made no such deduction. (Innes, 1965: 12±13)
The process of collecting data and creating theories can occur at the same
time. Some insights about data can only be made if the detective has prior
knowledge. In detective fiction, though, there is an end point ± the solution
± to a series of problems. There is a point in the detective narrative at which
148

a decision is made on how the observations and the relationships between
clues solve the case.
In this chapter we go a step beyond exploration of data. In quantitative
studies we often wish to explore the relationships between variables and to
fit those relationships to theories. We will investigate both the statistical side
and the theoretical side of this process.
LOOKING AT BIVARIATE DATA, CORRELATION AND REGRESSION
In the previous chapter we examined ways of exploring, describing and
summarizing data from a single variable ± univariate analysis of data. We
examined a range of graphical and numerical methods for representing
univariate data. But most variables do not exist in isolation. Social scientists
are often interested in the relationships between two or more variables. A
clinical psychologist may be interested in the relationship between depres-
sion and a schizophrenic's belief in hearing voices. This would be an ex-
ample of a bivariate analysis ± a study of the relationship between two
variables. The clinical psychologist may also be interested in the relation-
ship between more than two variables. We would then be involved in ana-
lysis of multivariate relationships.
It is beyond the compass of this book to cover the statistical techniques for
multivariate analysis, but we will explore the statistical techniques for ana-
lysing bivariate relationships. We will continue our investigation into the
role of graphical and numerical methods for describing variables and the
strength, relationship and direction of variables.
Plotting Bivariate Data
We can represent bivariate data (pairs of data values) graphically on a two-
dimensional plot known as a scatterplot. Scatterplots are also known as
scatter diagrams. The basic idea of a scatterplot is that each pair of data
values can be represented as a point on a two-dimensional plot. For
example, consider the hypothetical data in Table 6.1 for two variables X
and Y.
F I N D I N G A N S W E R S F R O M T H E I N Q U I R Y
TABLE 6.1 Hypothetical data
Person X Y
1 9 7
2 12 8
3 5 4
4 6 7
5 2 4
6 4 3
149

We can represent the data for person 2 as the set of coordinates (12, 8).
The number `12' means that the X value is 12 units along the measurement
represented by the X-axis; the number `8' signifies that the Y value is 8 units
along the Y-axis. The scale values for the X and Y-axes begin with 0. The
scatterplot in Figure 6.1 displays the bivariate Table 6.1 data.
Figure 6.1 shows that as the values of X increase, the values of Y increase
and vice versa. There is a positive relationship between X and Y. The statis-
tical sleuth might also find that a scatterplot for X and Y may show that X
and Y have a negative relationship. High values on one variable are associ-
ated with low values on the second variable, as in Figure 6.2
On the other hand, it may be difficult to see any systematic relation-
ship between X and Y, indicating that the two variables are not related
(Figure 6.3).
Scatterplots may also form a strong cluster, as though around a line,
indicating that the relationship between X and Y is linear. It is also possible
that the scatter forms a curve, indicating a non-linear relationship between
X and Y.
As we found in the last chapter, graphical techniques can also be useful in
identifying outliers or values that are very different from the general trend
0
1
2
3
4
5
6
7
8
9
0 5 10 15
X
y
FIGURE 6.1 Scatterplot for data inTable 6.1
0
2
4
6
8
10
0 2 4 6 8
FIGURE 6.2 Negative association between two variables
150

represented by the rest of the data. A scatterplot can also be used to identify
outliers, as you can see in Figure 6.4.
What should the data snooper do when there is evidence of outliers in the
data? The first step should always be to check the data for data entry errors.
There is nothing more frustrating than conducting a series of analyses,
agonizing over the interpretation of results that were unexpected, only to
find that the results are influenced by a data entry error. Check for mistakes
in recording the data. If you eliminate data entry error as an explanation for
the outlier, you should then check that the data themselves are valid, that is,
that the data points are faithful and accurate representations of the variables
being measured. If the data are valid then a detailed examination of the
outliers (and any other characteristics of the individuals whose data are
different) may lead to revision of the theoretical underpinning of the study.
The data snooper may also find that the points on a scatterplot cluster
into groups. This type of pattern may suggest that there are distinct groups
of individuals that should be analysed separately. Alternatively, it may
suggest the need for a third dimension (in other words another variable!)
to explain why the data are clustering.
Correlation: a Measure of Co-Relation
With scatterplots we pair one observation with another observation. From a
scatterplot we can identify trends and patterns among a collection of paired
FIGURE 6.3 No relationship between two variables
0
5
10
15
20
0 5 10 15
FIGURE 6.4 Scatterplot showing an outlier
151

observations. Scatterplots are a useful visual aid but it is also possible to
create a simple summary description (a numerical summary) of the degree
of relationship. This is the role of correlation.
Like the scatterplot, correlation is a relation ± a relation between paired
observations. Correlation is also concerned with covariation ± how two
variables covary. A psychologist may be interested in how delinquency
and parental bonding covary. If there is evidence of correlation and co-
variation between delinquency and parental bonding, our psychologist
may wonder whether delinquency can be estimated from parental bonding.
While correlation is concerned with the degree and direction of relation
between two variables, prediction is concerned with estimation, that is,
estimating one variable from another variable.
Historically, the concept of prediction precedes any mathematical or stat-
istical development of correlation. In 1885, Sir Francis Galton, a gentleman
scholar, published an influential paper titled `Regression towards medioc-
rity in hereditary stature' ± a paper that also had implications for the the-
ories of evolution for Galton's cousin, Sir Charles Darwin. Galton used
regression to refer to certain observations that he had made. He noticed
that tall parents did not always have tall offspring. In fact, on average,
the children of tall parents tended to be shorter than their parents; and
short parents tended, on average, to have taller offspring. Statisticians
now refer to this phenomenon as regression towards the mean. The term
regression no longer has the biological connotation. But Galton's ideas on
regression were developed by Sir Karl Pearson and resulted in a measure of
co-relation, namely the correlation coefficient. In fact, the most widely used
measure of correlation is known as the Pearson Product Moment Correlation.
We saw that certain features of bivariate data can be identified from a
scatterplot. We can see by eye whether two variables are positively or
negatively related, or if they are related at all. We can also establish whether
the relationship is linear. The correlation coefficient or simply correlation
is a numerical summary depicting the strength or magnitude of the
relationship that we see by eye, as well as a measure of the direction of
the relationship.
Variables like height can be measured in centimetres or inches. But in
measuring bivariate relationships we want to be confident that we can
measure the strength of the relationship between variables irrespective of
whether height is measured in centimetres or inches, or whether age is
measured in years or months, and so on. One way of removing the influ-
ence of scaling is to standardize the variables. To standardize a variable we
simply subtract from the variable score the mean of that variable and divide
by the standard deviation of that variable. If X is a variable with mean M
and standard deviation s, the standardized version of X, which we will
denote as ZX, is
ZX ˆ
X M
s
152

If John's exam score is 4, the mean of the exam scores is 5.75 and the
standard deviation is 2.11, then the standardized score would be 70.83.
John's score is, therefore, 0.83 standard deviations below the mean. The
Pearson Product Moment Correlation Coefficient or simply, Pearson's
correlation coefficient, is a numerical summary of a bivariate relationship.
It is defined in terms of standardized variables. Let ZX and ZY denote
the standardized variables for X and Y respectively. Pearson's correlation
coefficient, r, is defined as
r ˆ
X
ZXZY
n 1
where n is the number of pairs of observations. This measure is the average
product of the standardized variables. The coefficient, r, is obtained by
standardizing each variable, summing their product and dividing by
n 1. Some statistics texts will define r as
r ˆ
X
ZXZY
n
:
That is, n rather than n 1 will divide the sum of the product of standard-
ized variables. The latter formula is used if you are analysing a population.
The former equation is used if you are analysing a sample. We will return to
the distinction between samples and populations.
The process of standardizing scores was important in the development
of the correlation coefficient. Like the good, modern-day data snooper,
Galton began by producing a scatterplot of the parents and their respective
offspring. Galton's scatterplot was perhaps the first of its kind. He
standardized all heights. He then computed the means of the children's
standardized heights and compared them to fixed values of the standard-
ized heights of corresponding parents.
What Galton found was that the means tended to fall along a straight line.
What was more remarkable was that the each mean height of the children
deviated less from their overall mean height than the parents deviated from
their overall mean. There was a tendency for the mean height of the off-
spring to move toward the overall mean. This observation was in fact
an instance of a correlation that is not perfect. In fact, the correlation was
about 0.5 (Guilford, 1965).
There are many ways of re-expressing the formula for r. All of these
alternative formulae are equivalent. An alternative formula that is easier
computationally is
r ˆ
n
X
XY
X
X
X
Y

n n 1†sXsY
153

Having said that this equation is easier computationally, it is usual practice
to use a calculator, statistical package or spreadsheet program to compute r
rather than compute the coefficient by hand.
Example 6.1: Computing the correlation coefficient
Do sports psychologists become more effective as they become more experienced? A
university researcher studied a random sample of 10 psychologists, each of whom
was seeing athletes with similar problems. The researcher measured the number of
sessions needed for a noticeable improvement in athletes as well as the number of
years of experience for each sports psychologist. The data are presented in Table
6.2.Is there a correlation between years of experience and effective outcome?
TABLE 6.2 Hypothetical data on
correlation between years of counselling
experience and effective outcome
Years of experience No. of sessions
5 9
8 7
8 9
7 6
6 10
4 12
2 10
9 7
10 6
8 7
To find the correlation we use the formula:
r ˆ
n
X
XY
X
X
X
Y

n n 1†sXsY
Let years of experience be the variable X and number of sessions the variable Y.
We compute the standard deviations of X and Y and find that SX ˆ 2:45 and
SY ˆ 2:00.We also find that X ˆ 67 and Y ˆ 83 and XY ˆ 522.There are10
sports psychologists, n ˆ 10. Substituting these values into the correlation equation
we have:
r ˆ
10 522† 67† 83†
10 10 1† 2:45† 2:00†
r ˆ
341
441
r ˆ 0:773
154

The correlationbetweenyearsof experienceand numberof sessions is 0:773.There
is a strong negative correlation between these variables which indicates that more
experienced psychologists arrive at effective outcomes with clients in fewer sessions
than inexperienced psychologists.
The correlation coefficient has some important properties. The magnitude
of the correlation coefficient indicates the strength of the relationship
between the variables. The values of the correlation coefficient can range
from 1 to ‡1. A coefficient close to ‡1 or 1 indicates a strong relationship
between two variables. Values close to zero indicate the absence of a rela-
tionship between two variables. If the coefficient has a negative sign, then
the variables are negatively associated. If the coefficient has a positive sign,
then the variables are positively related.
Perhaps most importantly, and a fact that is sometimes overlooked by
inexperienced statistical sleuths, is that the correlation coefficient is a meas-
ure of linear association. In other words, if we were to fit a straight line
through the swarm of points on a scatterplot representing a perfect linear
association, all the points would lie on the line.
If the relationship is curvilinear, the correlation coefficient can be mis-
leading. Consider the scatterplot in Figure 6.5 for two variables X and Y.
X
5
4
3
2
1
0
1
2
3
Y
20
10
0
_
_ _ _
10
FIGURE 6.5 A curvilinear relationship
155

The plot suggests that the relationship between X and Y is not linear.
However, the correlation coefficient for these data is 0.73, suggesting a
strong linear association. But clearly the relationship is curvilinear, not lin-
ear. This shows the importance of plotting your data as one way of checking
that the underlying assumptions of a particular statistical procedure or
measure are met. It also shows the importance of not relying on just one
piece of evidence to make decisions!
In Chapter 5 we introduced the concept of resistant statistics. You will
recall that a resistant statistic is unaffected by extreme values. The correla-
tion coefficient is not a resistant statistic. Consider the hypothetical data for
two variables X and Y collected from seven people, shown in Table 6.3.
If we consider the data for the first six people we find that the correlation
between X and Y is 0.20. The data for seventh person represents a possible
outlier. If we include the data for the seventh person, the correlation coeffi-
cient is r ˆ 0:80. The inclusion of the outlier yields a strong correlation, but
when the outlier is omitted the correlation between X and Y is quite weak.
This example further highlights the importance of plotting data.
Introduction to Simple Linear Regression
Quite often social scientists are interested in predicting one variable based
on information from another variable. A psychologist, for instance, may be
interested in predicting coffee or tea consumption from work stress. In the
case of prediction, we then use the language of explanatory variable (work
stress) and response variable (coffee or tea consumption). The psychologist
may wish to go beyond simply saying that stress and caffeine consumption
are associated. There is a technique that allows us to describe the relation-
ship between explanatory and response variables in a linear form. This
procedure is known as simple linear regression.
Prediction and Correlation
Prediction and correlation are closely related concepts. If two variables X
and Y are unrelated, then knowing something about X tells us nothing
about Y. It is not possible to accurately predict Y from X in this situation.
In fact guessing would be as good a prediction as we could get! However,
if X and Y are related, then knowing something about X implies some
TABLE 6.3 Data with outliers
Person X Y
1 1 5
2 4 3
3 5 2
4 4 5
5 5 8
6 6 7
7 12 14
156

knowledge of Y. In this case, we can go beyond a simple guess and predict
Y from X with some accuracy. As the correlation between X and Y increases,
the accuracy with which we can predict Y from X also increases (Ferguson,
1959).
We need to be careful, however, about the meaning of the term `predic-
tion'. For the layperson, prediction implies being able to determine some-
thing exactly. In other words, it implies causation. Statistically, prediction is
closely related to estimation. Although we say that X predicts Y we must
remember that prediction is still based on correlation. We can predict some-
thing but only with a certain level of accuracy and confidence. We will
return to these and related issues later.
Method of Least Squares
We have used scatterplots to investigate not just the presence of a relation-
ship between two variables X and Y but also whether that relationship is
linear. If there is evidence of linearity, then the straight line is the simplest
way of describing Y from X. That is, we can model Y from X. The most
commonly used approach of modelling or fitting a line to bivariate data is
the method of least squares.
The method of least squares seeks to find a line of best fit through the
swarm of points on a scatterplot. But how do we define `best fit'? If we wish
to describe a line predicting Y from X then we position the line through the
points such that we minimize the sum of the squared distances taken
parallel to the Y axis from each point to the line. The idea is illustrated in
Figure 6.6.
The line passing through the points represents the predicted responses.
We use the symbolic language ^
y to denote these predicted responses. The
distance between a point and the line represents the difference between
predicted and observed y values, y ^
y. These differences are also referred
to as the residuals and are illustrated in Figure 6.7.
The method of least squares aims to fit a line so that the sum of the
squared residuals is minimized. In other words, if the line is a good
Y
X
Distance from point to
to Y axis
FIGURE 6.6 Fitting a line through points on a scatterplot
157

model (that is, good prediction) the residual values will be as small as
possible. The smaller the residuals the better the fit of the line to the data.
The general equation for a straight line is
y ˆ a ‡ bx
where a is the intercept and b is the slope of the line. The intercept is the
distance on the Y-axis from the origin to where the line cuts the Y-axis. In
other words, it is the value of Y when X ˆ 0. The slope of the line is an
indication of the rate of change of Y as X changes. That is, the rate of
increase in Y as X increases. It is beyond the scope of this introductory
book to present the mathematical derivation of the estimates of a and b
when the least squares method is applied. Suffice it to say that we can
calculate the values of a and b using the following equations:
b ˆ
X
xy
1
n
X
x
X
y

X
x2 1
n
X
x
2
a ˆ My bMx
where My and Mx are the means of the Y and X values respectively.
Statistical texts also represent the means of Y and X symbolically as
y and

x respectively.
Once we have estimated the values of a and b, we are in a position to
predict values of Y, ^
y. We can use the following equation, also known as a
regression equation, to predict ^
y:
^
y ˆ a ‡ bx
Y
X
data (x, y)
y
ŷ
y
y ˆ
−
FIGURE 6.7 Illustrating the concept of residual
158

Let's return for a moment to our psychologist who is interested in predict-
ing caffeine consumption from the amount of work stress. In this case, x
would represent known values of work stress. Stress might be measured
using an inventory, a test or set of tests, that yields scores between 0 and 20
where low scores indicate minimal stress and high scores high levels of
stress. Caffeine consumption is measured in terms of the number of cups
of tea or coffee consumed per day.
Let's now assume that the regression from predicting caffeine consump-
tion from stress scores is given by the regression equation, ^
y ˆ 3 ‡ 0:7x. We
interpret the slope of the line 0.7 to mean that there is a caffeine consump-
tion increase by 0.7 of a cup for every unit increase in the stress score. The
intercept, which has a value of 3, would be the caffeine consumption if a
person had a score of 0. We can also use this equation to predict values of
caffeine consumption from any value of work stress. For example, if a
person scores 12 on the work stress inventory, we can predict (on the
basis of the regression equation) that he or she consumes 11:4‰3 ‡ 0:7 12†Š
cups of coffee or tea per day.
Example 6.2: Finding the regression line
Let us return to the data inTable 6.2 and find the regression predicting the number of
sessions required for effective outcome in terms of years of experience. To find the
regression lineweneed to compute the constanta and theslopeb.Using the following
equations:
b ˆ
X
xy
1
n
X
x
X
y

X
x2 1
n
X
x
2 and a ˆ My bMx
We find that
P
XY ˆ 522,
P
X ˆ 67,
P
Y ˆ 83,
P
X2
ˆ 503 and
P
X†2
ˆ
4489.
Substituting these values into the formula for b we have:
b ˆ
X
xy
1
n
X
x
X
y

X
x2 1
n
X
x
2
b ˆ
522 67† 83†=10
503 4489†=10
b ˆ
34:1
54:1
b ˆ 0:63
159

a ˆ My bMx
a ˆ 8:3 0:63† 6:7†
a ˆ 12:52
Therefore our regression equation is^
y ˆ 12:52 0:63x.
The Statistical Inquirer multimedia courseware covers correlation and regres-
sion. Use the exercises in the course to further develop your skill in using
the statistic. Remember to use the dataset to assist the practice.
Assessing the Fit of the Regression Model
There are a number of ways of assessing how well our regression equation,
the model for predicting the response variable from the explanatory vari-
able, fits the data. We have already said that good prediction requires the
residuals to be as small as possible. If the regression model is adequate then
the predicted values based on the regression model will be close to the
actual values. In other words, when the statistical sleuth has an acceptable
regression model for bivariate data, the residuals will all be close to zero.
Having lots of large residuals is an indication that the model is not fitting
the data well. There may be instances where the model does not fit one or
two of the values. This is evidence that those values are potential outliers.
Residuals can be thought of as the error one makes in estimating the
values of a response variable ± they are errors of estimation. The standard
deviation of these errors is a handy measure of the accuracy of the estimate.
It is a measure of the accuracy of predicting the response variable Y from
knowing something about the explanatory variable X. This measure is also
known as the standard error of the estimate, syx, and is given the equation:
syx ˆ

X
y ^
y†2
n
s
The values for a response variable Y consist of two parts, a component that
is estimated, ^
y, and a component corresponding to the error of estimation,
y ^
y. If we think of the estimated value as the model for Y, and the error of
estimation as the residual, then any data point can be defined in terms of a
model component and a residual component.
Data ˆ model ‡ residual
The variances of the model and residual components are additive.
Moreover, the variance of a response variable is equal to the sum of the
variance of the model and residual components. In other words, the vari-
160

ance of Y, s2
y, is equal to the sum of the variance of the predicted value of Y,
s2
^
y, and the variance of the residuals, s2
yx. The ratio of the variance of the
predicted values of Y and the variance of the observed values of Y has a
special relationship with the correlation coefficient. The ratio of these
variances is equal to the square of the correlation coefficient:
r2
ˆ
s2
^
y
s2
y
This ratio shows the amount of variance of the response variable that is
explained by the regression model. This ratio is also known as the coefficient
of determination. It provides one way of assessing the adequacy of the regres-
sion model. If r2
is 0.70 we can state that 70 per cent of the variance in Y is
explained by the regression model. This result suggests that the regression
model is accounting for a considerable amount of the variance in the
response variable. In some texts the coefficient of determination is repre-
sented symbolically as R2
.
A final caveat! It is important that the data snooper considers all the
evidence available when making a decision about the adequacy of a regres-
sion line or model. Begin by looking at a scatterplot of the data to see if the
relationship is linear. Then examine the measures we have just discussed to
determine the `goodness' of fit of the regression line. More advanced and
detailed treatments of the topic of regression are available in texts by Draper
and Smith (1981), Kerlinger and Pedhazur (1973) and Cohen and Cohen
(1983).
Issue of Causation
We know that there is a correlation between smoking and lung cancer.
There is supporting evidence that heavy smokers tend to contract lung
cancer more frequently than do non-smokers (US Surgeon General, 1964).
But does smoking cause lung cancer? Most of the evidence is based on
correlational studies comparing cancer rates across different groups. Is
the existence of a correlation indicative of a causal relationship?
A correlation between two variables indicates a functional relationship.
The values of the response variable appear to be a function of the explana-
tory variable. But a correlation does not necessarily imply a causal relation-
ship between two variables. Indeed, it is usual for causal conclusions from
correlations to be met with severe criticism from the research community.
One reason for this criticism is the influence a third variable may have on
the correlation between variables X and Y. The claim that smoking causes
lung cancer, based on strong correlational evidence, is challenged by critics
who assert among other things that smokers on average are more stressed
and tense than non-smokers. Therefore we cannot rule out that it is stress or
tension that makes smokers vulnerable to lung cancer. In other words, the
161

correlation between smoking and cancer may be due to the influence of a
third variable, namely, stress.
There are a number of possible explanations as to why two variables, X
and Y, may be strongly associated (Moore and McCabe, 1993). The first
explanation is that X causes Y or Y causes X. Here the researcher would
need to establish that a change in one variable produces or causes a change
in the second. If smoking causes lung cancer then increased smoking will
result in lung cancer. The second type of explanation involves the presence
of a third factor, Z, influencing the relationship between X and Y. X and Y
may be related because X and Y respond to a third variable Z. In this case,
we may well be able to, say, predict Y from X, but there are instances where
changes to X will not necessarily result in a change in Y. Some researchers
have hypothesized that some people are genetically predisposed to certain
smoking behaviours and lung cancer. If a person is genetically predisposed
to cancer then changes to smoking behaviour will not change the likelihood
of contracting cancer.
Another possible explanation for a relationship between two variables is
that the effect of one variable on the second is confounded by the influence
of a third variable. It may be the case that smokers are more stressed than
the average person and therefore, the person is more vulnerable to cancer. It
may be that a person who smokes is less careful about their general health
and again may be more vulnerable to cancer than someone who is more
health conscious. In other words, it is difficult to see which variable is
actually associated with cancer. Smoking may be influential, but it would
be difficult to discern a causal link between smoking and cancer without
removing the influence of the confounding variable.
That said: don't smoke! In the case of research on smoking, there has also
been a build-up of various types of evidence, experimental, survey, and so
on, over time, that provides support for the causal hypothesis. We have
presented a simplistic interpretation of correlations linking smoking and
lung cancer. The situation is more complicated than has been presented
in this brief discussion. In general, causal statements based on single cor-
relations are fraught with danger. However, if there is evidence of patterns
of correlations linking two variables across different groups, then the pos-
sibility of a casual link increases. Statistical techniques such as regression,
particularly multiple regression, are useful in controlling for third variable
influences. In particular, the family of techniques known as structural equa-
tion modelling (SEM) allows the researcher to test and confirm models of
relationships between sets of variables, thus providing reasonable rejoin-
ders to critics proposing the influence of other variables. By using these
techniques we are able to statistically control and test the impact of other
variables. Although SEM techniques have grown in popularity, some
theorists have reservations on the indiscriminate or inappropriate use of
the technique. We are again reminded that a sound understanding of
statistical knowledge is essential for both interpretation and use of statistical
procedures.
162

USING SPSS: CORRELATION AND REGRESSION
To illustrate how SPSS provides correlation and regression, we will use
Patrick Rawstorne's dataset Predicting and Explaining the use of In-
formation Technology with Value Expectancy Models of Behaviour in
Contexts of Mandatory Use. This is the dataset provided in The Statistical
Inquirer for your practice.
The dataset examines the relationship between personality measures,
computer anxiety and subjective computer experience. One research ques-
tion of interest in this study is whether there is a relationship between
neuroticism and computer anxiety. To examine this question, we begin by
generating a scatterplot for neuroticism and computer anxiety. The two
variables are labelled `neurotic' and `anxiety1' respectively. We can generate
a scatterplot in SPSS by going to the Graphs menu and selecting Scatter.
Once you select Scatter, you will get the following dialog box.
Click on Simple and then choose Define. The next dialog box will ask you
to select the variables you wish to plot.
163

We wish to plot the variables `neurotic' and `anxiety1'. We select
`neurotic' and move it to the Y-axis box, and select `anxiety1' and move
it to the X-axis box. Click OK. These steps should generate the following
output:
ANXIETY1
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
NEUROTIC
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
164

This scatterplot suggests weak negative relationship between the two
variables. There is a tendency (weak though it may be) in these data for
less neurotic subjects to be more computer anxious. The correlation coeffi-
cient will provide a numerical summary of this relationship.
We can obtain a numerical summary of this relationship by computing
the correlation coefficient. To do this we select Correlate from the Analyze
menu and then choose Bivariate.
This option allows the user to run Pearson's correlation.
From the Bivariate Correlations dialog box, you select the variables `neur-
otic' and `anxiety1' and move them to the Variables window. Click on OK to
run the procedure and obtain the following output.
165

The correlation coefficient is 0:276, a weak negative correlation.
The output also gives the p-value associated with the correlation,
p ˆ 0:038. This value provides support for rejection of a null hypothesis
that the population parameter is equal to zero. The `null hypothesis' is
the hypothesis of `no difference'. The `p value' is the estimate that the
differences claimed by the hypothesis are significant. The convention is to
set the significance figure at less than 0.05 or 0.01. We will return to the
problem of hypothesis testing and significance in the section on samples
and populations.
Can we express the relationship between `neurotic' and `anxiety1' as a
straight line? Of course, this is done using regression analysis. To conduct a
regression analysis in SPSS, select Regression from the Analyze menu and
then choose Linear.
This selection will open the Linear Regression dialog box.
Correlations
NEUROTIC ANXIETY1
NEUROTIC Pearson Correlation 1.000 70.276*
Sig. (2-tailed) 0.038
N 57 57
ANXIETY1 Pearson Correlation 70.276* 1.000
Sig. (2-tailed) 0.038
N 57 60
* Correlation is significant at the 0.05 level (2-tailed)
166

We choose `neurotic' and move it to the Independent(s) window. This is the
explanatory variable. The variable `anxiety1' is the response variable or
dependent variable ± we move this variable to the Dependent window.
Click on OK to run the procedure. Below is some selected output from
the regression analysis.
This first output shows R2
and the standard error of the estimate. R2
is
0.076, indicating that only 7.6 per cent of the variance in `anxiety1' is
explained by `neurotic'. This value is low, suggesting that the fit of the
line to the data is not as good as it could be.
Model Summary
Adjusted Std. Error of
Model R R Square R Square the Estimate
1 0.276a
0.076 0.059 0.8512
a
Predictors: (Constant), NEUROTIC
Coefficientsa
Unstandardized Standardized
Coefficients Coefficients
Model B Std. Error Beta t Sig.
1 (Constant) 3.513 0.503 6.988 0.000
NEUROTIC 70.374 0.176 70.276 72.126 0.038
a
Dependent Variable: ANXIETY 1
167

This output window contains the values for the slope and intercept of the
regression line. The slope is also referred to as a regression coefficient. The
intercept is referred to as the constant. There are two types of regression
coefficient reported in this output, unstandardized and standardized. The
standardized coefficient is based on the standardized values of `neurotic'
and `anxiety1'. We will use the unstandardized coefficients to construct the
equation. The equation is ^
y ˆ 3:513 0:374x where ^
y ˆ `anxiety1' and
x ˆ `neurotic'.
Using Excel
We can construct a scatterplot in Excel by highlighting the variables you
wish to analyse by clicking on the column that defines the variable.
A scatterplot can be constructed by choosing the chart wizard and click-
ing on XY Scatter†. Simply click on Next until you reach the end of the step,
then click Finish.
Your output should now look as follows:
168

In order to use Excel to carry out a correlation analysis you will need to
ensure that the variables are in adjacent columns and that there are no pairs
of data with missing values. If you have missing values, as we have with the
computer anxiety data, then you should omit those pairs from the analysis
by deleting them. Once you have organized the data, you use the data
analysis tool package available in Excel to compute the correlation. You
select Data Analysis from the Tools menu.
From the Data Analysis dialog box select Correlation.
.00
1.00
2.00
3.00
4.00
5.00
.00 2.00 4.00 6.00
ANXIETY1
ANXIETY1
169

You will need to define the range of cells containing the data in the Input
Range window. This can be done by highlighting the data to be analysed.
Click on OK to compute the correlation.
A regression analysis is also relatively straightforward in Excel. From the
Tools menu select Data Analysis. From the Data Analysis dialog box choose
Regression.
170

In the Regression dialog box you need to define the cell range for the
response variable `anxiety1'. This variable is located in column D and the
data is in row 2 through to row 58, the range is $C2:$C58. This cell range is
placed in the Input Y Range window. The cell range for the explanatory
variable `neurotic' is placed in the Input X Range window. Click on OK to
run the simple linear regression. A snapshot of the output from the Excel
regression analysis is presented below.
LOOKING AT CATEGORICAL DATA
An important assumption underlying the correlation coefficient is that
the variables need to be continuous. There exist, however, a family of
techniques for examining the relationship between categorical variables.
Many studies in sociology and media studies involve the use of categorical
data. Before discussing these techniques we will consider some graphical
and tabular methods for exploring bivariate categorical variables.
EXPLORING BIVARIATE CATEGORICAL DATA
Table 6.4 describes the results of the 1836 Pinckney Gag rule, a rule of
historical importance because of its role in the antislavery petitions in the
US. US congressmen were classified according to the section of the country
they represented. These data are from Benson and Oslick (1969), reported in
Bishop et al. (1975: 99).
There are two categorical variables represented in Table 6.4, Vote and
Section. Vote has three categories or levels, yea, abstain and nay; the
171

variable Section also has three categories, North, Border and South. These
data can be represented graphically as a bar chart in Figure 6.8.
The vertical axis represents the frequency of responses. The horizontal
axis represents the three categories for Vote. Within each category of
Section, the three categories of the variable Vote are represented. The
chart is an effective way of displaying the frequency of voting pattern
within sections. However, a comparison of voting with each section is not
easy. If the voting data within each section are expressed as a percentage,
then a comparison is straightforward. Table 6.5 presents the frequencies
within each section expressed as a percentage.
A bar chart using the percentages in Table 6.5 is presented in Figure 6.9.
We note that fewer congressmen from the North voted for the rule, quite a
different interpretation from the bar chart for Table 6.4. A reading of the raw
frequencies shows that Northerners appeared to have more votes but
clearly there are more Northern congressmen. Interpreting the raw frequen-
cies is quite misleading!
TABLE 6.4 Distribution of votes by section
Distribution of votes
Section Yes Abstain No Total
North 61 12 60 133
Border 17 6 1 24
South 39 22 7 68
Total 117 40 68 225
Source: Bishop et al.,1975
0
10
20
30
40
50
60
70
North Border South
Yea
Abstain
Nay
FIGURE 6.8 Bar chart of frequency of votes by selection
TABLE 6.5 Percentage of votes
within each section
Section Yes Abstain No
North 46 9 45
Border 71 25 4
South 57 32 10
Source: Bishop et al.,1975
172

Plotting frequencies or relative frequencies can assist interpretation.
However, we should not disregard the utility of the tabular presentation
of these data. Tables such as Table 6.4 are like correlation tables. As with
correlation, we can ask whether the two variables in the table are indepen-
dent or associated in some way. Such tables are referred to as two-way tables
or contingency tables.
An important measure or statistic based on a contingency table is the chi-
square statistic or symbolically, 2
. The simplest form of a contingency table,
given in Table 6.6, consists of four cells based on two variables, each with
two categories, a 2 2 table.
Each cell represents the observed cell frequency corresponding to the ith
row of Variable 1 and the jth column of Variable 2. Symbolically, we can
represent the observed cell frequency as Oij. The row and column totals are
called marginals. There are situations in which we would like to compare
observed frequencies with theoretical or expected frequencies. For example, we
can compare observed frequencies Oij† with expected frequencies Eij†
based on the assumption that the two categorical variables are independent.
In the case where we are assuming independence, the expected cell frequen-
cies are given by:
Eij ˆ
RiCj
N
where Ri is the row total or marginal for row i, Cj is the column total or
marginal for column j, N is the total number of observations.
The chi-square statistic is used in situations where a comparison
of observed and expected frequencies is appropriate. This measure is
defined as:
0
20
40
60
80
100
North Border South
Yea
Abstain
Nay
FIGURE 6.9 Bar chart of raw percentage of votes by selection
TABLE 6.6 A 22 contingency table
Variable 2
Variable1 O11 O12
O21 O22
173

2
ˆ
X Oij Eij
2
Eij
That is, the measure is computed by finding the difference between
observed and expected frequencies for each cell, squaring these values
and dividing each difference by the respective expected frequency.
Finally, we sum over all possible cells.
The contingency coefficient is a measure of association between two cat-
egorical variables. This measure is based on the chi-square statistic:
C ˆ

2
N ‡ 2
s
where N is the total number of observations. Although a useful measure,
the contingency coefficient has one important limitation. The value of C is
dependent on the number of categories. That is, C derived from one 2 2
table can only be compared to a C value derived from another 2 2 table;
we cannot compare it to a C derived from a 3 3 table.
Example 6.3: Computing the contingency coefficient
A psychologist is interested in examining the relationship between success or failure
on a job and Emotional Competency (EC).One hundred employees are given an EC
test. The results are presented inTable 6.7.
TABLE 6.7 Data for job performance and
EC test
EC test
Job performance pass fail Total
success 15 35 50
failure 25 25 50
Total 40 60 100
The expected frequencies are computed using the equation
Eij ˆ
RiCj
N
For example, for cell (1,1) the observed value is15.The row total Ri for row1is 50.The
column total Cj for column1is 40. Therefore E11 ˆ 50 40†=100 ˆ 20.
174

The 2
statistic is given by:
2
ˆ
X Oij Eij
2
Eij
Table 6.8 sets out the computational details.
TABLE 6.8 Computational details for Table 6.7
O E OE† O E†2
O E†2
=E
15 20 75 25 1.25
35 30 5 25 0.83
25 20 5 25 1.25
25 30 75 25 0.83
100 100 0 4.17
Therefore, 2
ˆ 4:17.
The contingency coefficient is given by
C ˆ

2
N ‡ 2
s
C ˆ

4:17
4:17 ‡ 100
r
C ˆ

0:04
p
C ˆ 0:20
This results in a weak relationship between successful job performance and per-
formance on an EC test.
The chi-square statistic is one of the most important measures in statistical
theory. We will return to this measure and to contingency tables.
INFERENCE: FROM SAMPLES TO POPULATIONS
In Chapter 5 we described a set of descriptive summary measures for a
set of data. Those summary measures would be correct for those data,
provided that they were accurate. But our interpretation of the data
would be limited to that set of values. The statistical sleuth, indeed
any researcher, may want to make more general statements about the
variable(s) of interest that go beyond a limited set of values. A clinical
175

psychologist may be interested in the relationship between risk-taking
behaviour and parental bonding in 100 adolescents in Wollongong,
Australia, and describe the 100 adolescents. But clearly, the psychologist
might also like to make general conclusions about this relationship and
whether or not it holds among all Australian adolescents.
Statistical inference is that part of statistics that addresses the problem
of generalizing from results based on a particular small collection of
values to all possible observations that may be made about a variable or
variables. In Chapter 4, we used the term population to refer to the
potential set of values for an entity of interest. This set of values can be
large but finite, or it can be infinitely large. In many cases it would
be impractical, indeed impossible to observe all instances of the
population variable, and therefore, quite difficult to produce population
summary measures. The alternative strategy is to observe only a
limited set of values drawn from the population using an appropriate
selection method. We refer to this subset or subgroup of values as a
sample.
Values in a sample are only a selection from the population. It follows
that summary measures such as mean and variance of a sample of values
may be different from the summary measures based on population data. It
is also possible that summary statistics may vary for each sample drawn
from the population. None the less, each sample can be compared to the
population and so can be used to draw inferences about the population.
This is an important idea underlying statistical inference.
Parameters, Estimates and Statistics
Summary measures such as the mean and variance can be obtained for both
populations and samples. However, a distinction needs to be made between
the properties of populations and the properties of samples. We use the
term parameter to refer to properties of populations. The mean and variance
of a population are referred to as population parameters.
Samples are drawn from populations. Often we do not know the values
of population parameters. We can obtain summary measures for a sample
to say something about the population parameters. The sample measures,
however, are estimates of the corresponding population characteristics
or properties. Suppose, for example, that we sample 500 Australian
males, aged between 18 and 25 years, and ask them about their weekly
consumption of chocolate biscuits. Our findings yield that, on average,
young males consume 15.5 chocolate biscuits per week. This mean value
is an estimate of the population parameter. It is an estimate of the mean
weekly consumption of chocolate biscuits we would have obtained had we
been able to survey all Australian males aged between 18 and 25 years.
Measures based on or derived from sample information are referred to as
sample statistics.
176

A widely used convention is to use Greek letters to represent population
parameters and Roman letters to represent sample statistics. Thus we use
the Greek letter (pronounced mu) to represent the population mean. So far
we have used the letter M, or the symbol
X, to represent the sample mean.
Likewise, we have used the letter s to represent the sample standard devi-
ation. We use the Greek letter (pronounced sigma) to represent the popu-
lation standard deviation. We use the Greek letter (pronounced rho) to
refer to the population correlation, while the letter r symbolizes the sample
correlation.
Sampling Distributions
Sample statistics are estimates of population parameters. Each sample esti-
mate will vary from the population parameter. In other words, there is an
error in estimation associated with taking any sample. This error is referred
to as the sampling error. Sampling error will occur even with random
sampling.
When we talk about sampling error we also need to talk about sampling
distributions. For example, we could, theoretically, take all possible random
samples from the population of Australian men. Each sample would then
consist of N men. It is possible that we may actually have an infinite num-
ber of samples of size N.
We now compute the mean height, M, for each sample.
We can expect the mean of each sample to be different from each other
as well as different from the population mean. Some sample means will
be very different from the population mean and others will be very close
to the population mean. In short, we have a range of values of M: we will
have a distribution of sample means. We would then discover that a
small number of the sample means are very different from the population.
Most samples, though, will be close to the population mean. In other
words, what we would have arrived at is a frequency distribution of
sample means.
We might have drawn 193 samples with 20 men in each sample. We
calculate the mean height for each sample. Let's look at a hypothetical
frequency distribution of sample means.
Population
Sample with M1
Sample with M2
Sample with M3
177

Height (in cm) Frequency
155±159 5.00
160±164 6.00
165±169 9.00
170±174 10.00
175±179 15.00
180±184 30.00
185±189 45.00
190±194 35.00
195±199 20.00
200±204 10.00
205±209 5.00
210±215 3.00
The histogram for this distribution is presented below
An important feature of this distribution is that it appears normally distrib-
uted, a phrase used by statisticians to describe a curve which is symmetrical
and unimodal. Heights of people, for example, tend to be normally distrib-
uted. Furthermore, we can consider the likelihood or probability of each
mean value occurring. The probability that the man who is 210 cm is close to
HEIGHT
210.0
200.0
190.0
180.0
170.0
160.0
80
60
40
20
0
100
178

the mean of the distribution is very low. This distribution of sample means
and their respective probabilities is called the sampling distribution of the
mean. It is important to keep in mind that this is a distribution of values
and therefore it is possible to find the mean and variance of this distri-
bution.
Sampling distributions can be applied to other statistics, not just the
sample mean. For example, we can consider a sampling distribution for
the median. Provided that it is possible to obtain a sample statistic, then a
sampling distribution for that statistic is possible.
There are three very important properties associated with the sampling
distribution of the mean.
1 If we have a population with mean and we take random samples of
size N, then the mean of the sampling distribution of sample means is
equal to the population mean .
2 The variance of the sampling distribution of sample means will be equal
to 2
=N. That is, the variance of the sampling distribution will be equal
to the population variance 2
divided by N, the number of observations
in each sample.
3 Irrespective of the form of the population distribution, the sampling
distribution of the mean will approach the normal distribution, pro-
vided that the sample size N is sufficiently large. The closer the original
distribution is to the form or shape of the normal distribution, the less
the requirement that N be large.
The normal distribution is a very important mathematical distribution in
statistical theory. It is also referred to as the normal curve. The normal
curve, as mentioned, is unimodal (has just one mode) and is symmetrical,
as illustrated in Figure 6.10.
FIGURE 6.10 The normal distribution of a normal curve
179

Hypothesis Testing ^ Don't just show me the evidence, convince me that it
is so!
We can test whether a sample comes from a population. This is hypothesis
testing. To do this you will need a set of data, usually drawn from a random
sample. It is also important to know something about the underlying pro-
cess that generates the data ± a probability model for the data. You will need
to make some assertions about the population, particularly a population
parameter, like the mean. These assertions or statements are referred to as
hypotheses. There are usually two contradictory hypotheses, the null hypo-
thesis H0† and the alternative hypothesis HA†. The null hypothesis is
tested using the data. If we did not have any data on which to base our
test, then the assertion in the null hypothesis would be true.
The next step in the hypothesis-testing process involves computing one
or more statistics associated with the null hypothesis. On the basis of the
sample information we examine whether there is evidence supporting H0 or
refuting H0 and supporting HA. We retain H0 unless there is substantial
evidence to the contrary. We accept HA if the sample data challenges the
validity of H0.
What do we mean by substantial evidence? The traditional approach is to
assess the evidence against the null hypothesis using probability. How
likely are we to obtain an outcome based on the sample data that is different
from what we would expect if the null hypothesis were true? This prob-
ability is called the p-value of the test. Small p-values are evidence against
the null hypothesis (Hayes, 1988).
Hypothesis testing is used to test whether the data are consistent with a
single value of the population parameter. We might not be interested in
testing just a single value but rather identifying a range of parameter values
that are consistent with the data. In this case we should use an approach
known as confidence intervals. As the name suggests, a confidence interval
defines a range of values based on the sample data and the probability
value that the parameter of interest will fall within this interval. Before
returning to confidence intervals, let's look at some tests for samples.
One-Sample Tests
Let's start with statistical procedures used to make inferences about popu-
lations where we have information from one sample. Imagine an anthro-
pologist who is studying an isolated group of villagers on a remote island.
As part of this study she is interested in the literacy of the young adults on
the island. She measures the literacy of 100 young adults and finds that the
mean literacy for the young islanders is 105. Does this sample differ from
the general population? Let's assume that the population mean for literacy
is 100 with a standard deviation of 15.
How do we go about answering this question? The first step is to make
use of sampling distributions, in particular the sampling distribution of the
180

mean. We know that the sample mean has a distribution approximating the
normal distribution with mean and variance 2
=N.
We can translate the research question set by our anthropologist into a set
of hypotheses as follows:
H0 : ˆ 100
HA : 6ˆ 100
That is, if the null hypothesis is true then the population mean is 100.
To test the null hypothesis we use the Z-test. This test computes a Z
statistic given by:
Z ˆ

X
X

X
where
X is the sample mean,
X is the mean of the sampling distribution of
the mean and
X is the standard deviation of the sampling distribution of
the mean. The statistic Z is distributed as a normal distribution with mean 0
and standard deviation 1. Once we have calculated Z we can look up a set
of normal tables or use a computer to obtain the probability of finding a
standard norm value equal to or as low as the calculated Z.
For our example we have:
Z ˆ

X
X

X
where
X ˆ =

N
p
and N is the sample size.
Z ˆ
105 100
15=

100
p
Z ˆ
5
1:5
Z ˆ 3:33
The p-value associated with this Z is 0.0004. This result provides support
for the alternative hypothesis rather than the null hypothesis. Our anthro-
pologist can conclude that, in terms of literacy, her sample is different from
the standard population.
If our anthropologist wishes to construct a confidence interval for the
population mean, she can use the following formula:

X z

N
p
181

where z is the upper 1 †=2 critical value for a standard normal distri-
bution. We find these values from a set of tables. We provide some
commonly used values in Table 6.9
For our data the confidence level is given by 105 1:96†1:5 or between
102.06 and 107.94. That is, we can say with 95 per cent confidence that the
population mean lies in the interval 102.06 and 107.94.
Often we do not have complete information on the population para-
meters. What are the implications for using the Z-test when the population
standard deviation is unknown? It's time now to turn to history and
examine the work of William Gosset.
`It's not the drink I tell you!!' `These beer samples are not normally
distributed.'
William Gosset is credited with discovering the t-distribution. The
t-distribution is a very special distribution used in statistical testing. A
brewery employed Gosset in Dublin as a statistician. Why employ a
statistician? Gosset was required to examine the variability of beer. From
a quality control point of view his task was to identify ways of maintaining
variability within acceptable limits. He was hampered by two very import-
ant limits, small samples and not knowing the variability of the population
parameter. So if I take the Z statistic, what happens when I replace the
population parameter with an estimate of that parameter? Answer, the
resulting statistic is distributed slightly differently from the normal distri-
bution ± the t-distribution in Figure 6.11. However, what is interesting about
Figure 6.11 is that if the degrees of freedom increased, then the t-distribution
would start to resemble the normal curve. You start to get less and less
extreme scores in the tail as the sample gets bigger.
Let's consider again our anthropologist and assume that the population is
unknown. In this case we cannot use the Z-test. We use a one-sample t-test.
The form of the t-test is very similar to the Z-test. The only differences are
that we estimate the population using the sample standard deviation and
that the t-statistic is distributed as a t-distribution. The t-distribution shares
many features of the normal distribution. It is unimodal and symmetrical
but it is also leptokurtic, that is, it is more peaked than the normal distri-
bution. There is also a different t-distribution for each number of degrees of
freedom. Degrees of freedom refers to the number of values that are free to
TABLE 6.9 Some commonly used
values from a set of normal tables
Confidence level z
95% 1.96
99% 2.58
182

vary given certain restrictions imposed on the data. For the one-sample test,
the t-distribution has N 1 degrees of freedom.
The t-test is given by:
t ˆ

X
X
s
X
where s
X is the estimate of the standard deviation of the sampling distri-
bution defined as s
X ˆ s=

N
p
where s is the standard deviation of the
sample. In order to calculate s
X our anthropologist would need to compute
the sample standard deviation and divide this value by the square root of
the sample size. Once we have computed t, we can find the p-value associ-
ated with this value by consulting t-distribution tables.
The logic underlying the construction of a confidence interval for the
population mean when is unknown is similar to that when the parameter
is known. In this case, the confidence is given by

X ts
X
The value of t defining either 95 or 99 per cent confidence intervals varies as
the degrees of freedom vary. Consider a hypothetical example where

X ˆ 25:5, s ˆ 7 and N ˆ 16. The degrees of freedom in this example are
N 1 ˆ 16 1 or 15. Assume we wish to construct a 95 per cent confidence
interval, then the t value with 15 degrees of freedom is 2.13.
s
X ˆ s=

N
p
ˆ 7=

16
p
ˆ 1:75. Thus the limits of the confidence interval are
25:5 2:13 1:75† and 25:5 ‡ 2:13 1:75† or 21.77 and 29.23.
One-Sample Test for Categorical Data
In 1866 the botanist and monk Gregor Mendel reported the findings of his
experiments on hybridization of peas. In one experiment he observed the
FIGURE 6.11 The t-distribution
183

shape and colour of peas from a sample of plants. The hybrid plants were
crossed with each other and yielded 556 seeds, of which 315 were round
and yellow, 101 wrinkled and yellow, 108 round and green, and 32 wrinkled
and green. His genetic theory hypothesized that the expected frequency
should be in the ratio 9:3:3:1. Was he right?
Mendel's data are categorical. There are four categories of shape and
colour of peas, round and yellow, wrinkled and yellow, round and green,
and wrinkled and green. The null hypothesis is that the actual frequencies
will equal the expected frequencies across the genotypic categories. How do
we test this hypothesis? We test the null hypothesis by using the chi-square
statistic discussed earlier.
Like all the statistics we have discussed so far, the chi-square has a theor-
etical sampling distribution that is well known. The distribution is a func-
tion of degrees of freedom. There is a different sampling distribution for
each value of degrees of freedom. Furthermore, we can find a p-value for
any value of chi-square. The hypothesis-testing procedure is much the same
as that used with the normal and t-distributions.
Recall that the chi-square statistic is:
2
ˆ
X Oi Ei†2
Ei
where Oi and Ei are the observed and expected frequencies respectively
in the ith category. The expected frequencies for each cell is given by
Npi where pi is the probability of being in the ith cell and N is the total
number of observations or frequencies. The chi-square statistic has chi-
square distribution with C 1 degrees of freedom where C is the number
of categories.
The frequencies and computations are presented in Table 6.10.
The obtained chi-square value is 0.470. The p-value associated with
this value lies between 0.90 and 0.95. It follows that we have grounds for
retaining the null hypothesis. In other words, the sample data support
Mendel's theory.
TABLE 6.10 Frequencies in colour and shape of peas
Oi Ei Oi Ei†2
=Ei
Round yellow 315 312.75 0.016
Round green 108 104.25 0.135
Wrinkled yellow 101 104.25 0.101
Wrinkled green 32 34.75 0.218
Total 0.470
Source: Ferguson,1959:161
184

Two-Sample Tests
Test of Equality of Means for Independent Samples
Social scientists like to compare groups. Do men and women differ in their
attitudes to capital punishment? Do men and women differ in their voting
patterns? Do students who receive one-to-one tuition perform better at
statistics than students who do not? The main feature of all these questions
is that they involve the comparison of two groups. In this section we
describe a number of statistical tests that can be used to compare two
independent groups or samples.
A sports psychologist, Dr Sam Dunk, is interested in the effectiveness of
imagery as a preparation strategy on the accuracy of basketball free throws.
Ten players of equal ability are randomly assigned to two conditions (five
players in each condition). Players in the first condition receive no special
training while the players in condition 2 are trained in mental imagery.
After training each player is required to make 10 free throws; the score is
the number of successful attempts. The scores are in Table 6.11.
Does imagery training affect accuracy of free throwing?
We can attempt to answer this question by examining the mean free
throw score for each group. We can strengthen our argument by using
the t-test for independent samples. The basic idea underlying this test is a
comparison of means. If the training strategy is effective then the mean of
Group 2 should be significantly different from that of Group 1. If the strat-
egy is ineffective then the means will be similar. What we are actually doing
in this case is comparing two population means, by testing the null hypoth-
esis that the two population means are equal, H0 : 1 ˆ 2.
We can estimate the difference between the population means 1 2
using the difference between the sample means,
X1

X2. In order to use
this statistic inferentially we need to know its sampling distribution. From
this distribution we will be able to determine the probability of obtaining a
difference in drawing random samples of any size. The mean of the sam-
pling distribution of differences is equal to the difference of the population
means, 1 2. The variance of the sampling distribution of differences,
represented symbolically as 2

x1
x2
, is:
2

x1
x2
ˆ
2
1
n1
‡
2
2
n2
TABLE 6.11 Hypothetical data for number
of successful free throws in two conditions
No training Imagery training
6 6
4 8
5 9
5 7
5 8
185

where 2
1 and 2
2 are the variances of the populations. This sampling distri-
bution will be normal. If the population variances are unknown, then we
can use the sample variances to estimate the population parameters. This
estimate is
s2

x1
x2
ˆ
s2
1
n1
‡
s2
2
n2
The square root of this estimate (that is, the estimate of the standard devi-
ation of the sampling distribution) is the standard error of the difference of
the means. The ratio of the difference between the sample means and the
estimate of the standard error is the t statistic.
t ˆ

X1

X2
s2

x1
x2
In most texts this ratio is said to have a t-distribution with degrees of
freedom n1 ‡ n2 2. However, Moore and McCabe (1993) note that this
statistic does not have a t-distribution, but rather only approximates the
t-distribution. The t statistic will have a t-distribution with degrees of
freedom n1 ‡ n2 2 when the two population distributions have the
same standard deviations. In other words, both sample variances
approximate the population variance. In this case, the estimate of the
standard deviation can be expressed as a weighted average of the sample
variances.
sp ˆ

n1 1†s2
1 ‡ n2 1†s2
2
n1 ‡ n2 2
s
The pooled estimate assumes that the population variances are equal. This
assumption is known as the homogeneity of variance assumption, an important
assumption of the t-test for independent samples. The t statistic, when we
assume that the populations have the same variances, is:
t ˆ

X1

X2
sp

1
n1
‡
1
n2
r
Example 6.4: t-test for independent samples
A not sowell-knownSherlockHolmes case is that of whetherenvironmental tempera-
ture affects performance on a mental ability test.Two groups of people are randomly
186

assigned to two conditions ^ a hot condition and a condition in which it is cold.Scores
on the ability test are collected (high scores out of 20 indicate better performance)
and the summary statistics are reported in Table 6.12. Holmes decides that a t-test
for independent samples is needed!
TABLE 6.12 Descriptive statistics
Condition Mean Standard deviation Sample size
Hot 15.5 3.25 10
Cold 12.0 2.95 10
Holmes hypothesizes that:
H0 : 1 2 ˆ 0
HA : 1 2 6ˆ 0
Holmes should first compute sp.
sp ˆ

n1 1†s2
1 ‡ n2 1†s2
2
n1 ‡ n2 2
s
sp ˆ

10 1† 3:25†2
‡ 10 1† 2:95†2
10 ‡ 10 2
s
sp ˆ

173:385
18
r
sp ˆ

9:6325
p
ˆ 3:1036
Now Holmes can compute t.
t ˆ

X1

X2
sp

1
n1
‡
1
n2
r
t ˆ
15:5 12:0
3:1036

1
10
‡
1
10
r

t ˆ
3:5
1:388
t ˆ 2:52
187

Holmes notes that there are 18 degrees of freedom. The p-value for t ˆ 2:52 lies
between 0.05 and 0.01. He concludes that there is sufficient evidence to reject the
null hypothesis.On the basis of the sample information we can say that environment
does affect performance on an ability test.
Just as we define a confidence interval for the population mean, we can
also define a range of values that we say will contain the difference
between two population means with 95 per cent or 99 per cent confidence.
If we draw a random sample of size n1 from a population with unknown
mean 1 and we also draw a second sample of size n2 from a population
with unknown mean 2, and we assume that the populations have the
same variance, then we can define a 95 per cent or 99 per cent confidence
interval for 1 2 as

X1

X2† t sp

1
n1
‡
1
n2
s
The value of t comes from a t-distribution with n1 ‡ n2 2† degrees of
freedom.
From the example above, Sherlock Holmes could just as well have con-
structed a confidence interval for the difference of the population means.
The computations are presented below:

X1

X2† t sp

1
n1
‡
1
n2
s
ˆ 3:5 2:10 1:388†
ˆ 0:59 6:41
Therefore the difference between the population means will lie between
0.58 and 6.41 with 95 per cent confidence. The t-value with 18 degrees of
freedom is 2.10. Recall that our null hypothesis is H0 : 1 2 ˆ 0. The
value 0 (the value of the difference between the means when the null
hypothesis is true) is not contained in this interval. Therefore we have
supporting evidence to reject the null hypothesis.
If we assume that the population variances are unequal, then the con-
fidence interval is

X1

X2† t

s2
1
n1
‡
s2
2
n2
s
The degrees of freedom is this case are the smaller of n1 1 and n2 1.
188

The following table presents some values of t for constructing a 95 per
cent confidence interval.
df t df t df t
1 12.71 11 2.20 25 2.06
2 4.30 12 2.18 30 2.04
3 3.18 13 2.16 40 2.02
4 2.78 14 2.15 50 2.00
5 2.58 15 2.13 60 2.00
6 2.45 16 2.12 80 1.99
7 2.37 17 2.11 100 1.98
8 2.31 18 2.10 1000 2.813
9 2.26 19 2.09
10 2.23 20 2.09
Based on Griffiths,Stirling,Weldon (1998)
Rank Test for Independent Samples
The statistical tests we have considered so far involve assumptions about
the distributions of variables from populations. The Z and t-tests, for ex-
ample, assume that the populations from which the samples are drawn are
normally distributed. The statistical sleuth may on some occasions encoun-
ter situations where little is known about the population from which the
sample is drawn, or where there is evidence suggesting that the population
distribution is not normal. There is a family of tests that do not make
assumptions about the population distribution. These tests are referred to
as distribution free or non-parametric. We will now consider a test for two
independent samples. This test uses the ranks of values rather than the
actual scores. Therefore, it is usually referred to as a rank test.
In the rank test we would assume that a person has been randomly
assigned to a particular group. Assume for the moment that people are
not assigned to groups and we assume a rank, ri, to each of the scores,
xij. Next we return the scores to their original group. If the groups are
different, then the sum of the ranks or the average ranks for each group
will be different for each group. If the groups have similar scores then
the average ranks or sum of the ranks will be similar. Denote the sum of
the ranks as R1 and R2 respectively. We can test whether the groups are
different by applying the Mann-Whitney U test. We compute two values
U1 and U2:
U1 ˆ n1n2 ‡
n1 n1 ‡ 1†
2
R1
U2 ˆ n1n2 ‡
n2 n2 ‡ 1†
2
R2
where n1 and n2 refer to the number of observations in groups 1 and 2
respectively. We calculate a statistic U to be the smaller of U1 and U2.
189

The Mann-Whitney U test is used with small samples. For large samples
we can compute a z statistic defined as follows:
z ˆ
U n1n2=2

n1n2 n ‡ 1†
12
r
where n is the total number of observations. Once we have calculated this
value we can find the p-value associated with it. In the case of tied ranks the
formula for z is slightly different.
z ˆ
U n1n2=2†

n1n2
n2 n

n3
n
12
!
v
u
u
t
X
T
where T ˆ t3
t†=12, and t is the number of tied values.
Example 6.5: Rank test for two independent groups
Consider the following observations for two samples.
Sample1: 44 32 38 51 54 56 67 69 62 73
Sample 2: 6 10 13 14 29 42 26 46 50 55 70 77
We wish to test the hypothesis that the samples come from different populations.
We can use the test
z ˆ
U n1n2=2

n1n2 n ‡ 1†
12
r
to test this hypothesis. The first step is to rank-order the values and obtain the
following ranks.
Sample1: 10 7 8 13 14 16 18 19 17 21
Sample 2: 1 2 3 4 6 9 5 11 12 15 20 22
In order to compute U we need to compute U1 and U2.
U1 ˆ n1n2 ‡
n1 n1 ‡ 1†
2
R1
190

U2 ˆ n1n2 ‡
n2 n2 ‡ 1†
2
R2
Thesum of the ranks for sample1R1is143,while thesum of ranks for sample2R2 is110.
n1 and n2 are10 and12 respectively.
U1 ˆ n1n2 ‡
n1 n1 ‡ 1†
2
R1
U2 ˆ n1n2 ‡
n2 n2 ‡ 1†
2
R2
U1 ˆ 10 12† ‡ 10 11†=2 143
U1 ˆ 32
U2 ˆ 10 12† ‡ 12 13†=2 110
U2 ˆ 88
U is defined as the smaller of U1 and U2.So U ˆ 32. We now need to find z.
z ˆ
U nn2=2

n1n2 n ‡ 1†
12
r
z ˆ
32 10 12†=2

10 12† 22 ‡ 1†
12
r
z ˆ
28

230
p
z ˆ 1:85
The p-value associated with z is 0.0322.On the basis of this evidence we can retain
the alternative hypothesis. There is evidence that the samples come from different
populations.
Tests for Categorical Data
Guilford (1965: 234) cited the work of Baller (1936) who reported a study
that examined whether intelligence level was contingent on marital status.
The study reports two samples of 206 young American males. The men in
the first sample were regarded as feeble-minded in terms of IQ when they
were in school. The second group of men of similar age had IQ levels in the
normal range. The cross-tabulation of marital status and intelligence is
presented in Table 6.13.
191

You will recall that this is a two-way table or a contingency table. These
tables are useful for displaying the cell frequencies for two categorical vari-
ables. We can examine the cell frequencies and surmise whether one vari-
able is related to or independent of the second. Baller noted that the
proportions of married men were 0.408 and 0.539 for `feeble minded' and
normal categories respectively. Is this difference in proportions in marital
status statistically significant? To examine these questions we use the
chi-square statistic we introduced earlier in this chapter. The statistic is
2
ˆ
X Oij Eij
2
Eij
Under the null hypothesis of independence the expected cell frequencies
are equal to:
Eij ˆ
RiCj
N
where Ri is the row total or marginal for row i, Cj is the column total or
marginal for column j, N is the total number of observations. The chi-square
statistic has a chi-square distribution with r 1† c 1† degrees of freedom
where r is the number of rows and c is the number of columns. In the case of
Baller's data the degrees of freedom are 2 1† 2 1† ˆ 1. Once we have
calculated the statistic we can find its corresponding p-value.
For Baller's data we have in Table 6.14 a comparison of observed and
expected frequencies.
You can see from this table that, for each cell, we compute the value
O E†2
=E and then sum these values across the cells. The obtained
chi-square statistic is 7.10 in this case. The p-value associated with this
TABLE 6.13 Frequencies relating to marital status and IQ
Feeble-minded Normal Total
Married 84 111 195
Unmarried 122 95 217
Total 206 206 412
TABLE 6.14 Comparison of observed and expected frequencies for Baller's data
Cell O E O E† O E†2
O E†2
=E
Married, feeble-minded 84 97.5 13.5 182.25 1.87
Married, normal 111 97.5 713.5 182.25 1.87
Unmarried, feeble-minded 122 108.5 713.5 182.25 1.68
Unmarried, normal 95 108.5 13.5 182.25 1.68
7.10
192

statistic lies between 0.01 and 0.001. This result then supports the hypothesis
that married and unmarried differ significantly with respect to IQ!! Of
course, the statistical sleuth would ask if there is another explanation for
this result. Is there another variable that may be influencing the frequencies?
It is possible to examine the relationship among three or more categorical
variables simultaneously. The chi-square test for independence cannot be
used to examine more than two variables. If the researcher wished to look
at the interaction of three or more categorical variables then he or she would
need to refer to what are called log-linear models. Howell (1992) and Agresti
(1990) give excellent introductory accounts of these techniques.
Tests for Related Samples
We have discussed methods of comparing samples that are independent
of each other. Although the research design that generates these data
is common in the social sciences, we may also wish to use research
designs which generate data about the sample over time. For example, a
statistics lecturer may be interested in comparing performance on statistical
problems at different times of the day. He chooses two problems of equal
difficulty. One problem is given to students in the morning, the other
problem is given in the afternoon. That is, the same student completes
each problem. This is an example of a within-subjects design.
Consider a psychologist who is interested in the effectiveness of a treat-
ment for speech anxiety. Twenty volunteers agree to participate in the study.
All participants are initially tested for level of speech anxiety. On the basis
of this test 10 pairs of participants are identified where each member of the
pair has the same level of speech anxiety. One member of the pair is
assigned to a treatment condition and the other member of the pair to a
placebo condition. Each participant is then tested again on a speech anxiety
measure. Although the participants are assigned to different conditions,
they are still correlated or matched on initial level of anxiety. How does
our researcher test for group differences?
The data obtained from the designs can be analysed using a technique
called a related samples t-test. Consider N pairs of observations Xi, Xj†.
They might be two people paired or matched in terms of anxiety scores or
the observations may be paired because one observation has been taken in
the morning, the other in the afternoon. We can find the difference
between any pair of observations Xi, Xj†, and we will denote this difference
as D ˆ Xi Xj. Furthermore, we can find the mean,
D, of these differences.
As with other tests of significance we have discussed in this chapter, the
statistic
D has a sampling distribution. The estimate of the variance of
the sampling distribution of
D is
s2

D ˆ
s2
D
N
where s2
Dis the variance of the Ds:
193

s2
D ˆ
X
D2
X
D
2.
N
N 1
We can define the t statistic:
t ˆ

D
sD
t ˆ

D

S2
D
.
N 1
r
This statistic is distributed as a t-distribution with N 1 degrees of free-
dom. We should remember that the numerator of the t statistic is in fact

D 0. Let's return to one of our examples to see how this test is applied.
Consider again the psychologist who is interested in speech anxiety. The
scores on the anxiety test are in Table 6.15.
Our researcher hypothesizes that the two groups will differ in level of
anxiety. The null hypothesis then is H0 : 1 2 ˆ 0. That is, the difference
in the population means is zero.
In order to apply the t-test we need to compute D.
Treatment condition Placebo D D2
23 24 71 1
20 26 76 36
24 27 73 9
26 22 4 16
18 20 72 4
19 19 0 0
17 20 73 9
15 25 710 100
25 21 4 16
21 27 76 36
TABLE 6.15 Hypothetical data for
speech anxiety scores in two conditions
Treatment condition Placebo
23 24
20 26
24 27
26 22
18 20
19 19
17 20
15 25
25 21
21 27
194

We find the
D ˆ 23=10 ˆ 2:3. The variance of D is
s2
D ˆ
X
D2
X
D
2.
N
N 1
s2
D ˆ
227 23†2
.
10
10 1
s2
D ˆ 19:344
We now compute t:
t ˆ

D

S2
D
.
N
r
t ˆ
2:3

19:344
.
10
r
t ˆ 1:654
This t statistic is distributed as a t-distribution with N 1 ˆ 9 degrees of
freedom. The p-value associated with this obtained t statistic lies between
0.10 and 0.20. On this evidence we should retain the null hypothesis and
conclude that the treatment has not affected speech anxiety.
Rank Test for Correlated or Related Samples
The Wilcoxon signed ranks test is a distribution-free alternative to the
t-test for related samples. This test is based not on the difference between
pairs of scores, but rather the ranks of the differences. Difference scores
are ranked with respect to their magnitude, but not their sign (whether
they are positive or negative). Once we have ranked the difference scores
we re-assign the signs, and compute the sum of the positive difference
scores, T1, and the sum of the negative difference scores, T2. We now
compute a statistic T that is the smaller of T1 and T2. There are 2N
possible
signed ranks in this example. Assuming that each pair of scores is random,
then each of the 2N
sets of ranks is equally likely. Consider the case where
N is 5. In this case we have 32 sets of possible ranks. The probability that T1
is zero is 1/32, the probability that T1 is 1 is also 1/32. The probability that
T1 is either 0 or 1 is 2/32. This pattern is also the same for T2. Furthermore,
the probability that either T1 or T2 is 0 is 2/32. It is therefore possible to
195

construct a table of probabilities for any sample size ± this is the sampling
distribution for T (Roscoe, 1975).
Under the null hypothesis of no difference between groups, one would
anticipate that T1 and T2 would be the same. In this case the value of
T would be maximal. However, if the groups are different, then there
will be a tendency for either T1 to be greater than T2 or vice versa. T
will tend to be smaller and equal 0 when the two samples are maximally
different.
To see how the Wilcoxon signed rank test is applied let's consider the
speech anxiety example discussed earlier. Recall that we are hypothesizing
that the two distributions are the same under the null. A table of difference
scores and their ranks is provided below.
D Rankof D Pos Neg
71 1 1
76 7.5 7.5
73 3.5 3.5
4 5.5 5.5
72 2 2
0
73 3.5 3.5
710 9 9
4 5.5 5.5
76 7.5 7.5
T1 is 11 and T2 is 34. Note that on one the difference score is 0. We do not
count zero differences; we also reduce N by the number of zero differences.
For this example N is now 9. T is the smaller of T1 and T2; T is 11. For N ˆ 9
the p-value is greater than 0.05. Therefore there is evidence to retain the
null. The two distributions are similar. We arrive at a similar result to the
related samples t-test.
USING SPSS AND EXCEL: ONE-SAMPLE TESTS
Let's see how we can use SPSS and Excel to do one-sample tests. Let's again
use Patrick Rawstorne's computer anxiety data, provided in The Statistical
Inquirer. Patrick's data in the data file were collected from 60 undergraduate
students. Assume that the mean population age of undergraduate students
in Australia is 24. We can test whether the sample in this data file comes
from this population.
Using SPSS we select One-Sample T-Test from the Compare Means option in
the Analyze menu.
196

This selection will produce the One-Sample T Test dialog box.
We select the variable Age and move it to the test variable(s) window and
type the value 24 in the Test Value window. Click OK to run the procedure.
Selected output from this procedure is presented below.
One-Sample Test
Test Value ˆ 24
95%
Confidence
Interval of the
Difference
Sig. Mean
t df (2-tailed) Difference Lower Upper
AGE 1.361 59 0.179 1.6167 70.7610 3.9943
197

This output gives us the t statistic, which is 1.361, and its corresponding
p-value of 0.179. Convention is to reject the null hypothesis when the
p-value of the obtained statistic is less than 0.05. This result provides
support for the null hypothesis that the sample is from a population with
mean 24.
We can conduct a one-sample z-test in Excel using the function ZTEST.
Earlier in this chapter we noted that when the population variance is
unknown we can estimate it using the sample variance. The resulting stat-
istic is only distributed as a normal distribution when the sample size is
large. Otherwise the new statistic is distributed as a t-distribution. SPSS
does not offer a z-test for population means. The reader should note that
the ZTEST function should be used with large samples when the population
variance is unknown. Running the function ZTEST is quite straightforward.
Click on the Paste Function button located at the top of the Excel window.
Select Statistical from the Function Category window and ZTEST from the
Function name window. This will produce a ZTEST dialog box.
198

In the Array window you will need to define the cell range containing
the data for the variable AGE. In the X window we insert the test value
(population mean) 24. The third window Sigma refers to the population
standard deviation. If it is known, the user can insert the value in this
window. If this window is left blank, the sample standard deviation will
be used. Note that the p-value is 0.0839. On the basis of this result we
retain the null hypothesis. The sample comes from a population with
mean 24.
In this chapter we also discussed the chi-square test for goodness of fit ± a
one-sample test for categorical data. In Excel we could use the function
CHITEST to conduct such a test. However, the function requires that the
user provide the actual and expected cell frequencies in an Excel worksheet
in order to conduct the test.
Conducting the goodness of fit chi-square test using SPSS is less
complicated. One of the variables in the computer anxiety data is the
average time spent on a computer. This variable is categorical, with six
categories: Almost never, Less than 30 mins, from 30 mins to 60 mins, 1±2
hours, 2±3 hours, and More than 3 hours. Let's test the hypothesis that the
expected frequencies will be equally distributed over the categories. To run
this test in SPSS we select Chi-square from the Nonparametric option in the
Analyze menu.
This will open the Chi-square test dialog box.
We select the variable of interest and move it to the Test Variable List
window. Notice that under Expected values there are two radio buttons,
one labelled `All categories equal' and the other labelled `Values'. To test
our hypothesis we leave the default option `All categories equal'. It is
possible to specify the theoretical frequencies by clicking on the Values
199

option, entering the values one at the time, and remembering to click on
Add after each entry. To run the procedure click OK. The output will look as
follows:
The first output window gives observed and expected frequencies. The
second output window gives us the obtained chi-square value (which is
41.6 in this case), the degrees of freedom and the p-value. Note that the
p-value is 0.000. We have support for rejection of the null hypothesis and
Average time spent per day
Observed N Expected N Residual
Almost never 1 10.0 79.0
Less than 30 mins. 7 10.0 73.0
From 30 mins to 60 mins 22 10.0 12.0
1±2 hours 21 10.0 11.0
2±3 hours 4 10.0 76.0
More than 3 hours 5 10.0 75.0
Total 60
Test Statistics
Average time
spent per day
Chi-Squarea
41.600
df 5.00
Asymp. Sig. 0.000
a
0 cells (0.0%) have expected frequencies less than 5.
The minimum expected cell frequency is 10.0
200

concluding that the responses are not equally distributed across the cat-
egories of our variable.
USING SPSS AND EXCEL: TWO-SAMPLE TESTS
We will use the Accounting for Tastes dataset, tastes.sav, in order to show how
SPSS and Excel can be used for comparing two population means. We will
start with a t-test for two independent samples. The hypothesis we wish to
test is whether males and females differ in terms of their annual incomes. To
test this hypothesis using SPSS we click on the menu Analyze, select Compare
means and then choose the option Independent Samples T Tests.
This option will open the following dialog box.
As with most procedures in SPSS we select the variable of interest, in this
case `jobinc', and move it to the Test Variable(s) window. Next we select the
variable `sex' and move it the Grouping Variable window. You need to click
on the Define Groups button, opening the following window.
201

Given that Sex is coded 1 for females and 2 for males, we insert the
value 1 in the Group 1 window and 2 in the Group 2 window. Click
Continue followed by OK to run the procedure. The following output will
be produced.
From this output we see the mean annual incomes for females (sex ˆ 1)
and males (sex ˆ 2). In the output table titled `Independent Samples Test',
we first note that the test for homogeneity of variance (known as Levene's
test) is significant. This indicates that population variances are different.
The t statistic in this case is 717.761 with a p-value of 0.000. We reject
the null hypothesis of equality of population means and conclude that
the mean annual incomes of males and females are different. By looking
at the means we see that males earn more than females.
If we assume that the data violate distributional assumptions (population
distributions are not normally distributed), then we would use a non-
Group Statistics
Std. Std. Error
SEX N Mean Deviation Mean
Annual job income 1.00 1405 14052.06 15208.8114 405.7487
2.00 1313 27427.44 22989.0154 634.4363
Independent Samples Test
Levene's Test
for Equality
of Variances t-test for Eq
Sig.
F Sig. t df (2-tailed)
Annual job income Equal variances 131.784 0.000 717.998 2716.000 0.000
assumed
Equal variances 717.761 2252.592 0.000
not assumed
202

parametric test instead of the traditional t-test to test whether the distribu-
tions for annual income differ for males and females. To conduct this test
using SPSS we select 2 Independent Samples from the Nonparametric Tests
option in the Analyze menu.
This opens a dialog box similar to that in the case of the independent
samples t-test.
We select the dependent variable and place it in the Test Variables window,
select the independent variable and place it in the Grouping Variables win-
dow and define each level of the groups as before. Note that the Test Type
has been checked as Mann-Whitney U, which is the test we wish to conduct.
Click OK to conduct the test. The output is shown below.
203

The first table presents the mean and sum of the ranks. In the second
table we have the Mann-Whitney U statistic, the z statistic and the
p-value associated with the z. The p-value is very small, providing
support for rejecting the null hypothesis. Men, on average, earn more
than women.
To illustrate using Excel to perform the two-sample test, we will return
to the computer anxiety dataset. In this case we may be interested in
investigating whether males and females differ in terms of computer
anxiety. We select the Data Analysis option from the Tools menu and then
select t-test: Two-sample Assuming Equal Variances. In the next dialog box you
will need to insert the cell ranges defining the data for the males and
females respectively. In this dataset we have a single variable for `anxiety1',
the computer anxiety measure, and a variable `sex' defining the gender of
each case. The data for the males is located in the first 23 rows, the data for
the females in the next 37 rows. When the cell ranges have been defined,
click OK to run the procedure.
Ranks
SEX N Mean Rank Sum of Ranks
Annual job income 1.00 1405 1119.30 1572610.00
2.00 1313 1616.54 2122511.00
Total 2718
Test Statisticsa
Annual job
income
Mann-Whitney U 584895.00
Wilcoxon W 1572610.0
Z 716.556
Asymp. Sig. (2-tailed) 0.000
a
Grouping Variable: SEX
204

The output is presented below.
We can see that the output contains the mean and variance for
males (variable 1 in the output) and females (variable 2). The t
statistic (71.489) is also presented along with its p-value (0.071).
Convention requires that the p-value be less than 0.05 in order to reject
the null hypothesis. In this case, the p-value is greater than 0.05, so we
retain the null.
Comparing the means of two related samples is quite simple in SPSS.
Students in the computer anxiety study were tested twice on the variable
ànxiety1'. Data for time 2 computer anxiety is labelled ànxiety2'. In other
words, the scores for ànxiety1' and ànxiety2' are correlated because it is
the same person responding twice.
In order to run a related samples t-test we select the Paired-Samples T Test
from the Compare Means option in the Analyze menu.
205

In the Paired-Samples T-Test dialog box we select the pair of variables we
wish to analyse.
We select `anxiety1' and `anxiety2' and then click on the arrow button
to move this pair of variables to the Paired Variables window. Click OK
to run the procedure. The output generated by this procedure is
presented below.
Paired Samples Test
Paired Differences
95% Confidence
Interval of the
Difference
Std. Std. Error Sig.
Mean Deviation Mean Lower Upper t df (2-tailed)
060E-02 0.4332 5.689E-02 73.33E-02 0.1945 1.417 57 0.162
206

As you can see, this output provides the t-value and the p-value associ-
ated with the t statistic. The p-value is large; we retain the null hypothesis
and conclude that computer anxiety has not changed over time.
The Wilcoxon signed rank test is the non-parametric equivalent of
the related samples t-test. To run the Wilcoxon test we select 2 Related
Samples.
This step opens the following dialog box.
We select the pair of variables in the same way as we did with the
parameter test and move them to the Test Pair(s) List. Click on OK to
run the procedure. The output is presented below.
207

The mean and sum of ranks are presented, along with the z statistic and
its p-value. As we can see, the p-value is large and consequently we retain
the null hypothesis ± men and women do not differ in terms of computer
anxiety.
We can use SPSS to test the independence of two categorical variables.
With the computer anxiety data we can test whether responses on the
frequency of computer use differ across males and females.
We begin by selecting cross-tabs from Descriptive Statistics from the
Analyze menu.
Ranks
Mean Sum of
N Rank Ranks
ANXIETY2 ± ANXIETY1 Negative Ranks 33a
27.73 915.00
Positive Ranks 21b
27.14 570.00
Ties 4c
Total 58
a
ANXIETY2 ANXIETY1
b
ANXIETY2 ANXIETY1
c
ANXIETY1 ˆ ANXIETY2
Test Statisticsb
ANXIETY2 ±
ANXIETY1
Z 71.488a
Asymp. Sig. (2-tailed) 0.137
a
Based on positive ranks.
b
Wilcoxon Signed Ranks Test
208

We select the variable `sex' and place it in the Row(s) window, and move
the variable `Use' (Frequency of Use) to the Column(s) window.
By clicking on the Statistics button we can choose to compute the
Chi-square statistic along with a number of other measures of association
for categorical data, including the contingency coefficient.
By clicking on the Cells button we can select an number of options,
including obtaining expected and observed cell frequencies.
Click Continue and then OK to obtain the following output.
In the first table we have the observed and expected cell frequencies. In
the second table we have the chi-square statistic and its associated p-value
(called Pearson Chi-square in the output). This p-value is smaller than the
conventional 0.05; we can conclude that the two variables are related. We
also obtained row percentages and from these percentages we can see that
males tend to spend more time using computers than females.
209

Sex of Participant * Frequency of use Crosstabulation
Frequency of use
A few A few About Several
times times once times
a month a week a day a day Total
Sex of Participant Female Count 2.2% 24.2% 7.2% 4.2% 37.2%
Expected Count 3.1% 17.9% 9.9% 6.2% 37.0%
% within Sex 5.4% 64.9% 18.9% 10.8% 100.0%
Participant
Male Count 3.2% 5.2% 9.2% 6.2% 23.2%
Expected Count 1.9% 11.1% 6.1% 3.8% 23.0%
% within Sex 13.0% 21.7% 39.1% 26.1% 100.0%
Participant
Total Count 5.2% 29.2% 16.2% 10.2% 60.2%
Expected Count 5.0% 29.0% 16.0% 10.0% 60.0%
% within Sex 8.3% 48.3% 26.7% 16.7% 100.0%
Participant
Chi-Square Tests
Asymp. Sig
Value df (2-sided)
Pearson Chi-Square 10.609a
3 0.014
Likelihood Ratio 11.098 3 0.011
Linear-by-Linear 3.460 1 0.063
Association
N of Valid Cases 60.000
a
3 cells (37.5%) have expected count less than 5. The
minimum expected count is 1.92
210

We can use Excel to conduct a related samples t-test. Let's again use the
variables `anxiety1' and `anxiety2'. Go to the Tools menu and select Data
Analysis. We then select t-Test: Paired Two Sample for Means.
Once we have chosen the option from the Data Analysis window, it will
open the next dialog box.
We define the cell ranges for each variable in the usual way and then
click OK.
In our discussion on the goodness of fit chi-square statistic we mentioned
we could use the CHITEST function to conduct that test. This function can
also be used to test the independence of two categorical variables. We have
opted not to illustrate this procedure, for the same reasons given in the one-
sample case.
INTRODUCTION TO RANDOMIZATION TESTS
In recent times, there has been an increasing interest in exploring alternative
approaches to computing statistical significance in cases where there is
evidence that the population distributions are not normal or the random
sampling assumption has been violated. The techniques underlying
these approaches are not new (see Edgington, 1964, for example). The
resurgence in interest is due in part to the speed with which modern
desktop computers can process quite computationally intensive techniques.
In particular, randomization tests have gained popularity. Randomization
21
1

tests are computationally intensive, but they do not require the assumption
that samples are randomly sampled.
With the tests we have considered in this chapter, we derived a p-value
for a test statistic by comparing it to its sampling distribution when the null
hypothesis is true. These sampling distributions are theoretical, and to use
them appropriately we need to ensure that certain assumptions are met ±
normality assumptions, homogeneity of variance assumptions, to name but
two. The idea underlying randomization tests is to construct an empirical
distribution for the statistic based on permutations of the data. The number
of permutations possible will in part be determined by the research design.
Sometimes the number of permutations is very large and we choose a ran-
dom sample of permutations to construct our permutation distribution.
Hypothesis testing with randomization tests is similar to `traditional'
testing ± tests based on normal theory. The decision to retain or reject the
null hypothesis is based on determining whether the obtained statistic or a
value that is more extreme under the null hypothesis is uncommon.
We will use an example from May and Hunter (1993) to illustrate the logic
of randomization tests. Assume we have two samples, with values 4, 5, 6 in
one sample and 1, 2, 3 in the second sample. The mean of the first sample is
5.00; the mean of the second sample is 2.00. We are interested in seeing
whether the means of these samples are different.
We begin by obtaining all possible permutations of the six scores 1, 2, 3, 4,
5, and 6 into two samples. We then compute the test statistic for each
permutation ± the mean difference. The results of these steps are presented
in Table 6.16.
TABLE 6.16 All possible permutations of six scores in two conditions
Permutation Sample1 Sample 2 Statistic: M1 M2
1 1,2,3 4,5,6 73.00
2 1,2,4 3,5,6 72.34
3 1,3,4 2,5,6 71.66
4 1,2,5 3,4,6 71.66
5 1,2,6 3,4,5 71.00
6 1,3,5 2,4,6 71.00
7 2,3,4 1,5,6 71.00
8 1,3,6 2,4,5 70.33
9 1,4,5 2,3,6 70.33
10 2,3,5 1,4,6 70.33
11 2,3,6 1,4,5 0.33
12 2,4,5 1,3,6 0.33
13 1,4,6 2,3,5 0.33
14 1,5,6 2,3,4 1.00
15 2,4,6 1,3,5 1.00
16 3,4,5 1,2,6 1.00
17 2,5,6 1,3,4 1.66
18 3,4,6 1,2,5 1.66
19 3,5,6 1,2,4 2.34
20 4,5,6 1,2,3 3.00
Source: Mayand Hunter,1993
212

From this table we can construct frequency and relative frequency dis-
tributions for the possible values of M1 M2, the difference between the
two sample means. The permutation distribution for these data is presented
in Table 6.17.
This distribution is an `empirically-derived' sampling distribution. We
can use it to determine the `p-value' for a value of a statistic. We can see
that for a mean difference of 3 the p-value is 0.05.
For a thorough treatment of randomization tests, we refer the reader to
Edgington (1995), Manly (1991) and May and Hunter (1993). There are a
number of commercially available packages and freeware programs for
conducting randomization tests. A brief review of these programs is pre-
sented by Hayes (1998). Hayes also presents some SPSS procedures for
randomization tests.
GREAT SOCIAL BIOLOGY DETECTIVE STORIES: `WE MUST HUNT
FOR CASES'
The statistical equations that we have introduced to you are general meas-
ures, nomothetic measures, that assume that the data, the individual cases,
form into patterns or distributions that are meaningful. But we have to be
very careful not to impose order on data where there is none or to assume
that distributions themselves create social or psychological order.
Income, for example, may form a normal distribution in a study, but it
does not follow that the distribution became that way because of a normal
curve. We look for patterns in the data and statistical measures assist us
with interpreting those patterns.
Early work on statistics, including the use of statistics in sociology,
reflected this tension between finding order and imposing order. Sociologists
and psychologists, for example, have long been interested in the role of
social or hereditary factors in influencing behaviour. Some of the most
TABLE 6.17 Permutation distribution for
data inTable 6.16
M1 M2 f p Cumulative p
73.00 1 0.05 1.00
72.34 1 0.05 0.95
71.66 2 0.10 0.90
71.00 3 0.15 0.80
70.33 3 0.15 0.65
0.33 3 0.15 0.50
1.00 3 0.15 0.35
1.66 2 0.10 0.20
2.34 1 0.05 0.10
3.00 1 0.05 0.05
Source: Mayand Hunter,1993
213

famous statistical measures were developed and applied in pursuit of fan-
ciful ideas about the possibility of a `super race', how genetics determines
social order. Others, like Durkheim, were interested in statistics for the
reverse reason, how social order determines behaviour.
Is There An Ideal Person?: Quetelet, Galton, Pearson
The normal distribution is attributed to Gauss and Laplace, but Adolph
Quetelet carried out an early application of the normal distribution to social
and biological data. Quetelet was a great promoter of the use of statistical
methods in Europe. He encouraged the use of accurate statistical records for
social phenomena such as births and deaths and crimes, as well as weather.
Quetelet found that the heights of French conscripts could be described
using the normal curve. The normal curve suggested to Quetelet the pos-
sibility of what he called the ideal observation, the mean, and the fact that
some observations deviated from this ideal. Quetelet came up with the idea
of the l'homme moyen, the average person as nature's ideal (see Hankins,
1968).
But it is not clear that Quetelet's research on biology can simply be trans-
lated to sociology and psychology. To what extent can the normal dis-
tribution be described as a model for the variability of social and
psychological phenomena? To what extent is the normal distribution a `nat-
ural' model of social and psychological data? The idea of the normal curve
has become so common in the modern research language that it is almost a
given. However, even statisticians such as Karl Pearson (who reported in
Biometrika in 1903 that cranial widths demonstrated the characteristics of a
normal curve) cautioned against the universal application of the normal
distribution. `The reader may well ask . . . is it not possible to find material
which obeys within probable limits the normal law? I reply, yes, but this law
is not a universal law of nature. We must hunt for cases [emphasis added]' (cited
in Yule and Kendall, 1937: 186).
Let's look at some theorists who hunted for cases. Galton argued along
evolutionary grounds that most human individual differences were inher-
ited. He proposed the science of eugenics and the possibility of creating a
super race through genetic manipulation. Galton set up a battery of tests.
He was fanatical about counting and measuring. Some of the variables he
measured in his `anthropometric laboratory' included height, arm span,
swiftness of blow and colour discrimination.
Galton had data for well over 9,000 individuals. He needed some way of
summarizing these data, and in particular, summaries that would support
his hereditarian hypothesis. He wanted to demonstrate the degree of simi-
larity of measures between brothers and unrelated persons. He created
scatter plots of bivariate data and identified a near straight-line relationship.
Galton set the seeds for the development of the correlation coefficient and
simple linear regression.
214

The concept of regression, or reversion, as Galton first called it, began
with his work with non-human material. Galton's work started with breed-
ing sweet peas. He started weighing thousands of pea seeds and selecting
different weights. He also started measuring their diameters, which he
found to be proportional to their weights. Galton sent samples of seeds
varying in weights to colleagues to plant. The results of his research were
reported in 1877 and suggested that the daughter seeds were not as extreme
as the parent seeds. The seeds had `reverted' to the average type of the
parent seed.
Galton noted that for every unit increase in the parent seed, there was on
average only a one-third increase in the unit size of the offspring seeds. This
observation was the genesis of the concept known as regression towards the
mean.
It was the application of this concept to human data that was of most
interest to Galton. He began the human side of his investigation with the
heights of parents and their children. He plotted the data, as we noted
earlier in this chapter. He found that the human offspring tended to regress
toward the mean, much in the same way that seed offspring did.
Galton then took the mean heights of parents and plotted this against the
heights of their children. He found that he could draw a line through the
scatter of points on his plot. This, of course, was the beginning of the
regression line. Galton found that children of taller parents were not as
tall on average as their parents, and children of shorter parents were not
as short. But this finding was somewhat paradoxical. It appeared not to
support the idea of full hereditary transmission of human characteristics
and qualities.
Does a General Intelligence Factor Exist?: Spearman and the introduction of
correlation
Charles Spearman made use of the correlation coefficient to propose a two-
factor theory of intelligence. Guilford (1954: 472) stated that `No single
event in the history of mental testing has proved to be of such momentous
importance as Spearman's proposal of his famous two-factor theory in
1904'. When Spearman tested people on various measures of cognitive
abilities, he found that the correlations among the measures were almost
always positive. People who scored high on one test tended to score high on
the others. Spearman argued that performance on these tests was governed
by one general characteristic, general intelligence factor. To account for the
less perfect correlations between tests, Spearman proposed the existence of
a task-specific factor.
Spearman's theory was based on an observation that various measures of
performance or ability are positively correlated ± a phenomenon termed
positive manifold. Spearman explained this observation by arguing that
all tests are influenced by this general factor, which he termed the psycho-
metric g or just g. For example, if we administer three ability tests, say,
Numerical Reasoning, Vocabulary and Mechanical Reasoning, we will
215

invariably find that these measures are positively correlated. This correla-
tion, Spearman would argue, is due to a more general factor, a general
mental ability factor.
The intercorrelations among a set of tests can be represented as a
matrix. Consider a correlation matrix reported by Spearman (1927:
147) in his famous book The Abilities of Man. In the table below we have
the correlations among five tests, Mathematical judgment, Controlled
association, Literary interpretation, Selective judgment and Spelling
administered to 757 participants (the results are from Bosner, 1912, cited
in Spearman, 1927).
1 2 3 4 5
1 Mathematical judgment 7 0.485 0.400 0.397 0.295
2 Controlled association 0.485 7 0.397 0.397 0.247
3 Literary interpretation 0.400 0.397 7 0.335 0.275
4 Selective judgment 0.397 0.397 0.335 7 0.195
5 Spelling 0.295 0.247 0.275 0.195 7
Source: Spearman,1927
Spearman made another very important observation about these correla-
tions and other correlation matrices of this type. He noticed that, once the
values in the matrix had been re-arranged, the size of the correlations
tended to decrease as you moved from left to right in a row and from top
to bottom as you moved down a column. For example, in the row for the
test Spelling, the correlations go from 0.295 to 0.195 as you move from left to
right along the row, and if you look at the column for Selective judgment
you will see that the correlations decrease from 0.397 to 0.195. This pattern
in the data led Spearman to postulate that there was an hierarchical order-
ing in the correlation matrix. He found that this pattern also showed that
the tests varied in the amount of factor g they revealed. Correlations among
tests to the left shared more of the factor g than tests to the right. In other
words, a correlation matrix is hierarchically ordered if the size of the cor-
relations decreases as you move from left to right in the correlation
matrix and the correlations are all positive.
Spearman needed a way of demonstrating this concept of hierarchy
mathematically. He noticed that if you partitioned the correlation matrix
so that you looked at only four tests at a time, something interesting could
be observed. He found that the difference of the products of the diagonal
entries of the matrix tended to be 0 if the pattern in the overall matrix
suggested an hierarchical ordering. He called this value the tetrad
difference. Consider the following a partition of the correlation matrix pre-
sented earlier.
216

Mathematical judgment Literary interpretation
Selective judgment 0.397 0.335
Spelling 0.295 0.275
The tetrad difference is 0:397 0:275† 0:335 0:295† ˆ 0:010. Indeed
most of the tetrads would be close to zero. Spearman had therefore found
an empirical method (based on correlations) for determining if a correlation
matrix was hierarchically ordered, and more importantly, a pattern of
results that could be explained by his two-factor theory (Rogers, 1995).
Is There a Genetic Component to Intelligence? Did Burt clone the data? ^ data
ain't always data!!
But is intelligence determined by the environment a person is reared in or is
it determined by genetics? How do we study the degree to which herit-
ability contributes to intelligence? This is one of the most important and
contentious issues surrounding the study of human intelligence ± the nat-
ure/nurture debate. Studies interested in the nature/nurture debate have
often used twins, in particular identical twins reared apart, to discover
influences of genetics and environment. Identical twins share the same
genotype. If one were to find a substantial relationship between measures
of intelligence of identical twins reared apart, then this would provide
support for a genetic theory of intelligence.
The work of Sir Cyril Burt provided the most promise for resolving the
nature/nurture debate. Burt's methodology was to examine identical twins
reared apart, but also to compare the data obtained from these twins to
other categories of paired children, such as identical twins reared together,
non-identical twins reared together, siblings reared apart, siblings reared
together, and unrelated children reared together. By using this meth-
odology, the question of whether intelligence was genetically determined
would be well and truly answered, or at least so Burt thought.
Burt and his co-workers tested numerous children in London. In 1943,
Burt reported that the correlation on a measure of intelligence among a pair
of 62 identical twins reared together was 0.86. He also reported a correlation
of 0.771 based on the another sample of 15 identical twins. These results
were exciting for the supporters of a genetic theory of intelligence. At last
there was evidence supporting the theory. However, there was something
fishy about the results being presented by Burt. Burt appeared to consis-
tently report a correlation of 0.771 for identical twins reared apart.
Moreover, there was amazing similarity in several of the correlations Burt
was reporting. For example, in 1955, Burt reported that on a group test of
intelligence for twins reared together, the correlation was 0.944; for identical
twins reared apart the correlation was 0.771 and for unrelated children
reared together the correlation was 0.281. Exactly the same correlations
(to 3 decimal places!) were again reported in 1966. In addition, the 1955
217

study reported correlation of 0.490 and 0.563 for tests of reading and arith-
metic respectively for siblings reared apart. The same correlation appeared
in the 1996 study for the same group ± the only difference was that the
sample size had increased from 131 in 1955 to 151 in 1966!!
Burt's views on intelligence were controversial, but his data raised extra,
more serious questions. Was this a case of scientific fraud or just a case of
sloppiness? Kamin (1974) noted the remarkable consistency in Burt's results
and questioned their veracity. Indeed, in 1976, Oliver Gillie, a medical
reporter for the London Times, placed an ad in the paper asking if
Margaret Howard or J. Conway could please contact him. Howard and
Conway were research assistants who assisted Burt and their names
appeared in some of the journal articles. No one replied. It was alleged
that the two women did not exist and that Burt had made up the data to
fit his genetic theories of intelligence. Abelson (1995: 102) argues that per-
haps Burt was treated unfairly. Abelson noted:
There is a benign explanation of the identity between early and late results,
despite added cases. A reasonable conjecture is that not all of the measures
were administered to the new cases. Because cases were hard to find, it is not
unlikely that some compromises were made in the interest of fattening the total N.
One such compromise might have been to omit some of the measures on some
batches of cases. . . . But this case makes the point that something that looks fishy
might be okay (albeit poorly set forth by an author who did not make clear what
was going on). Thus one should not be too quick to cry fraud.
Here then we have a case of detection where the statistical sleuth has looked
at a set of results and found something fishy. In the Burt example, there was
too much consistency in the results. In most of our research we look for
replication of results. By replicating certain results we provide evidence for
the validity of those results. But as students of statistics we are aware of
the concept of variability. We may obtain similar results, but possibly not
identical results (Rogers, 1995).
Are Social Factors More Important than Individual Inclinations? Durkheim's
study on suicide (The use of secondary data)
Emile Durkheim held that social groups have a collective inclination for
action, quite their own, and are the source of all individual inclinations,
including suicidal actions (1897). He is the opposite of the statisticians cited
above. Durkheim argued that biological, psychological and social psycho-
logical factors remain constant from one group to another or from one time
to another.
Durkheim lived at the same time as Sherlock Holmes. Sociology was not
taught as a discipline in Holmes's day. Durkheim was, therefore, one of the
first theorists to try to define the discipline and to distinguish it from other
disciplines such as philosophy and psychology.
218

Durkheim was a sleuth. He saw the incongruous. He noticed that
phenomena like suicide were intensely personal. What more personal,
and individual, an act could there be? Suicide appeared to be an intensely
personal act that involved complex personal decision-making before a deci-
sion to die was made. A person's own psyche, own feelings, surely, dictated
the course of action. Durkheim noticed, however, not only the incidence of
suicide but rates of suicide. He saw patterns in the data that showed that
suicides appeared to occur in the same proportions for different social
groups over time. How could this be? Do different social groups, like doc-
tors, set a quota of suicides each year?
Durkheim was a data collector and a creative problem-solver. His sec-
ondary data analysis drew on 26,000 cases of suicide that were classified
separately by age, sex, marital status and the presence or absence of chil-
dren. `M. Mauss alone performed the heavy task' (1970: 39). The statistics
were taken from official reports held by the Bureau of Legal Statistics, and
other official and academic sources.
Let's start with Durkheim's conclusions before examining some of the
data that he analysed:
Victims of suicide are in an infinite minority, which is widely dispersed; each one
of them performs his act separately, without knowing that others are doing the
same; and yet, so long as society remains unchanged the number of suicides
remains the same. Therefore, all these individual manifestations, however inde-
pendent of one another they seem, must surely actually result from a single group
of causes, which dominate individuals. Otherwise how could we explain that all
these individual wills, ignorant of one another's existence, annually achieve the
same end in the same numbers? At least for the most part they have no effect upon
one another; they are in no way conjoined; yet everything takes place as if they
were obeying a single order. There must then be some force in their common
environment inclining them all in the same direction, whose greater or lesser
strength causes the greater or less number of suicides. Now the effects revealing
this force vary not according to organic and cosmic environments but solely
according to the state of the social environment. This force must then be collective.
In other words, each people has collectively an inclination of its own to suicide, on
which the size of its contribution to voluntary death depends. (Durkheim, 1970:
304±5)
This short narrative is both a theoretical hypothesis and a conclusion in
Durkheim's study. Figure 6.12 maps his `cause and effect' statement.
Let's use Durkheim's examples from the statistics to show why he arrived
at this theoretical model. When Durkheim summarized the suicide statistics
by religion, for example in Table 6.18, he found that `everywhere without
exception, Protestants show far more suicides than the followers of other
confessions' (1970: 154). The difference varied between a 20 to 30 per cent
minimum and a maximum of 300 per cent. Jewish people committed sui-
cide less than Catholics and Catholics less than Protestants. But why? Was
the difference based on prohibition of suicide? No. Both Catholicism and
219

Protestantism penalized suicides `with great severity' (1970: 157). What,
then, made the difference? `The only essential difference between
Catholicism and Protestantism is that the second permits free inquiry to a
far greater degree than the first' (1970: 157). `Free inquiry', though, was for
Durkheim only the effect of another cause. Catholicism has fewer common
beliefs and practices than Protestantism. It has a creed, a set of beliefs, that
tie the group together and there is therefore a greater the integration of the
group: `the greater the concessions a confessional group makes to indi-
vidual judgement, the less it dominates lives, the less its cohesion and
vitality' (1970: 159). Durkheim concluded, therefore, `that the superiority
of Protestantism with respect to suicide results from its being a less strongly
integrated church than the Catholic Church' (1970: 159).
We can now break down Durkheim's more general theoretical hypothesis
into a more specific hypothesis, represented in Figure 6.13. The higher the
integration of a social group, the lower the suicide rate.
Durkheim extended this idea of integration to other statistics and other
social groups. For example, from Tables 6.19 and 6.20, Durkheim concluded
that `it appears that marriage has indeed a preservative effect of its own
against suicide' (1970: 198). Coefficient of preservation is the ratio of the
suicide rates of two groups of the same age and sex. For example, if the
suicide rate of unmarried men were 400 per million and that of married
men of the same age only 100 per million, then the coefficient of preserva-
tion would be 3. The lower the suicide rate of a group, the higher its
coefficient.
Collective tendencies Suicide
FIGURE 6.12 Durkheim's theoretical hypothesis on suicide
TABLE 6.18 Suicides in different countries per million persons of each
confession (adapted from Durkheim,1952:154)
Protestants Catholics Jews
Austria (1852^9) 79.5 51.3 20.7
Prussia (1849^55) 159.9 49.6 46.4
Prussia (1869^72) 187 69 96
Prussia (1890) 240 100 180
Baden (1852^62) 139 117 87
Baden (1870^4) 171 136.7 124
Baden (1878^88) 242 170 210
Bavaria (1844^56) 135.4 49.1 105.9
Bavaria (1884^91) 224 94 193
Wuttemberg (1846^60) 113.5 77.9 65.6
Wuttemberg (1873^6) 190 120 60
Wuttemberg (1881^90) 170 119 142
220

For Durkheim, marriage and domestic society, like religious society, is a
powerful counteragent against suicide.
Durkheim found something else happening with marriage statistics. The
greater the number of divorces, the greater the number of suicides. He did
not call this phenomenon `disintegration', but an aspect of `regulation'. The
statistics on the relationship between divorce and suicide did not mean that
there were more bad wives or husbands, but that the customs and laws
surrounding marriage and divorce had changed. `Divorce is never granted
except out of respect for a pre-existing state of customs. If the public con-
science had not gradually decided that the indissolubility of the conjugal
bond is unreasonable, no legislator would never have thought of making it
easier to break up' (1970: 273). When divorce takes a legal form it weakens
the moral structures assisting integration. The law assists, does not restrain,
suicide.
Durkheim created the construct anomy to describe the changes in `reg-
ulation' and the weakening of social group norms. Figure 6.14 summarizes
this second major hypothesis that relates to the idea of collective tendencies.
Degree of integration Suicide
FIGURE 6.13 Durkheim's hypothesis of degree of integration
TABLE 6.19 Influences of the family on suicide, unmarried men (adapted from
Durkheim,1970:197^8)
Coefficient of preservation in
Suicide rate relation to unmarried men
Unmarried men 45 years old 975 . . .
Husbands with children 336 2.9
Husbands without children 644 1.5
Unmarried men 60 years old 1,504 . . .
Widowers with children 937 1.6
Widowers without children 1,258 1.2
TABLE 6.20 Influences of the family on suicide, unmarried women (adapted from
Durkheim,1970:197^8)
Coefficient of preservation in
Suicide rate relation to unmarried women
Unmarried women 42 years old 150 . . .
Wives with children 79 1.89
Wives without children 221 0.67
Unmarried women 60 years old 196
Widows with children 186 1.06
Widows without children 322 0.60
221

Both integration and regulation contributed towards suicide and both make
up the collective tendency. Durkheim labelled the different types of suicide
according to the degree and overlap of integration or regulation. An unmar-
ried person who committed suicide might be labelled an ègoistic suicide',
because that person no longer had his or her original basis for existence in
life. A divorced person might be labelled an ànomic suicide' because the
social activity, marriage, lacked its original regulation. Durkheim also iden-
tified a third type of social cause of suicide ± àltruistic suicide' ± where
individuals are obliged to kill themselves. `Celts were known who bound
themselves to suffer death in consideration of wine or money' (1970: 222).
Altruistic suicide represents overly strong regulation of individuals; for
example, the Hindu requirement that widows commit ritual suicide upon
the funeral pyre. Where there is excessive regulation, the demands of
society become so great that suicide varies directly rather than inversely
with the degree of integration. Durkheim uses statistics from military sui-
cides to show that the officer corps, because of the honour code, has higher
suicides than lower ranks. The officer corps, highly integrated, should, one
would suppose, have fewer suicides than other ranks.
Durkheim's category of àltruistic suicide' shows us that he was acutely
aware of the problems with different types of claims made by the ìndi-
vidual' and by `society'. His theories appear very conservative but in his
private life he would, by modern standards, be defined as liberal.
Integration and regulation are `functions' in Durkheim's work. They are
real social causes that exist independently of a person's individual psycho-
logy. They form the basis of the `collective tendencies' that deliver the
proportion of suicides that we can observe in suicide rates. But these `func-
tions' affect more than one social act, like suicide. In Durkheim's theory
they affect all society.
Durkheim, of course, did not escape criticism or critique. Like Sherlock
Holmes, he was captured by the biases and prejudices of his day. `Women's
sexual needs,' says Durkheim, `have less of a mental character because,
generally speaking, her mental life is less developed' (1970: 272). Women
have `no great intellectual needs' (1970: 166). Such assumptions, one would
assume, would affect Durkheim's perceptions about the constructs that he
created. But the problem of `definition' and `constructs' goes further. The
very records that Durkheim relied on can be problematic. Durkheim was
not interested in the ìdiographic'. He did not investigate the definitions
that individuals or groups involved might apply to the `suicide act'. He did
not interview relatives and friends caught up in the death ± or the police
and the courts. All these people or groups might affect what ended up being
Degree of regulation Suicide
FIGURE 6.14 Durkheim's hypothesis of degree of regulation
222

a `suicide statistic'. `It has been repeatedly pointed out by scientific students
of the problem that suicide cannot be subject to statistical evaluation, since
all too many suicides are not reported as such. Those who kill themselves
through automobile accidents are almost never recorded as suicides; those
who sustain serious injuries during an attempt to commit suicide and die
weeks or months later of these injuries or of intercurrent infections are
never registered as suicides; a great many genuine suicides are concealed
by families; and suicidal attempts, no matter how serious, never find their
way into the tables of vital statistics' (Zilboorg, cited in Durkheim, 1970: 18).
Durkheim's work, despite flaws, shows the benefits in using secondary
data. There is a range of formal agencies in modern societies that collect
data on topics ranging from suicide to number of cars in each household.
There is also a range of studies, like Durkheim's, that can be revisited and
mined ± for critique or for extension.
SUMMARY
The good statistical sleuth does not treat statistical distributions as universal
laws. `We must hunt for cases', says the famous statistician, Karl Pearson
(cited in Yule and Kendall, 1937: 186). Famous statistical measures were
developed in response to an interest in fundamental issues surrounding
human behaviour. Famous sociological theories were developed in
response to interpretations of statistical evidence.
Quantitative research methods in social science research are often
involved in the investigation of relationships between variables. The idea
of correlation is central to this type of inquiry. The correlation coefficient
provides a summary measure of the extent and direction of the relationship
between two variables. This is a nomothetic approach to understanding
association. But the origin of the correlation coefficient lies in the scatterplot
which is idiographic in nature, plotting individual data points. Indeed the
identification of outliers (individual data points that don't fit the trend!) is
an important reason for constructing a scatterplot.
Correlation is closely related to prediction and statistical regression.
Prediction is estimation. What regression allows us to do is to make an
estimate that is better than simply an educated guess. Regression is a
way of modelling data. Implicit in the idea of a model is error. Prediction,
therefore, may not be precise. What the statistical sleuth tries to do is to get a
model of the relationship between variables that best fits the data. The
sleuth must remember that a linear model with just one explanatory vari-
able is the simplest possible model and that care must be taken about any
causal statements based on correlation models.
Correlation studies the relationship between variables. Inference allows
the sleuth to generalize results from samples to populations ± from the
particular to the general. We considered one-sample tests for comparing
223

whether a sample comes from a population with certain characteristics, as
well as two-sample tests ± tests that allow us to make statements about the
population means based on sample evidence. These are nomothetic tests ±
making generalizations about averages, not individuals.
We also investigated non-parametric or distribution-free tests. These tests
do not make assumptions about the distribution of the population para-
meter. Distribution-free tests are not used as often in the social sciences as
they could be or should be. For example, Micceri (1989) wrote an influential
paper in which he presented strong evidence that commonly measured
variables (including achievement and personality) in psychology are not
normally distributed. Yet traditional techniques continue to be used. One
reason why traditional tests such the t-test are commonly used is that they
are robust ± they seem to be reasonably accurate even when distributional
assumptions are violated. None the less, we are keen for the reader to
explore the alternative methods, especially randomization tests. These
tests are useful not only when distributional assumptions are violated but
also when the assumption of random sampling has also been violated.
Quetelet, Galton, Pearson, Spearman, Burt and Durkheim are all ex-
amples of the application of statistics to specific problems. Sometimes the
statistical sleuth ends up with good statistics that do not support the theory
± this is a good, not a bad, outcome. Sometimes the statistical sleuth, like
Durkheim, develops an interesting theory, but the collection and origin of
the statistics themselves become an issue.
The Statistical Inquirer provides additional lessons on correlation and
regression. Use these lessons to better understand both the formula and
their application.
MAIN POINTS
. A scatterplot is a graphical representation of the relationship between
two variables. We can use scatterplots to check for trends and patterns in
the data, and in particular, linear trends.
. Correlation is a numerical summary of the extent and direction of the
relationship between two variables. The correlation coefficient ranges
from ±1 to 1. A correlation of 1 indicates perfect positive linear correla-
tion; a correlation of ±1 indicates perfect negative linear correlation.
. A contingency table is a useful way of cross-tabulating frequencies from
two categorical variables. The chi-square statistic is used to test for
evidence of independence of two categorical variables.
. Statistical inference allows the researcher to generalize findings from
samples to populations. The concept of a sampling distribution is im-
portant in statistical inference. We make decisions about the null
hypothesis by determining whether the obtained statistic is relatively
rare or common in the sampling distribution of that statistic.
224

. One-sample tests such as the z test and the one-sample t-test are used to
test whether a sample is drawn from a population with certain para-
meter values. The chi-square test for goodness of fit allows comparison
of actual frequencies with theoretical or expected frequencies.
. We can compare two independent samples and make conclusions about
their respective parent populations using the t-test for independent
samples. The Mann-Whitney U test is a distribution-free alternative to
the independent samples t-test.
. If samples are related or matched then the related samples t-test
allows us to test whether the population means are equal or not. The
Wilcoxon signed rank test is the distribution-free analogue of the
related samples test.
. The independence of two categorical variables can be tested using the
chi-square test.
. Randomization tests are useful alternatives to traditional statistical tests
when distributional assumptions and random sampling assumptions
have been violated.
REVIEW EXERCISES
1 A psychology department decides to evaluate the performance of
its lecturers. Each lecturer teaches one subject. The department
measures each lecturer on (1) the average grade for students com-
pleting the subject on a scale of 0 to 10, and (2) a measure of overall
quality of lecture presentation on a scale from 0 to 5 (low scores
indicating poor quality). The data are collected from 10 lecturers
and presented below.
Mean grade Mean quality rating
9.8 4.5
8.0 4.0
4.4 3.0
6.4 3.5
5.1 2.0
6.8 3.0
5.7 1.5
5.0 3.5
8.0 4.0
7.5 6.0
(a) Plot the relationship between mean quality of lecture rating
and mean grade scores. How would you describe this rela-
tionship?
225

(b) Compute the correlation coefficient for quality of lectures and
grade score. Interpret the correlation coefficient.
(c) Using quality to predict grade scores, find the equation of the
form Y ˆ a ‡ bX which makes the best prediction.
(d) What is your best estimate of the expected mean grade when
the quality rating of lecturers is 2.5?
2 Explain in your own words what is meant by the standard error of
the estimate of Y.
3 In a study linking criminality and identical versus fraternal twins,
15 identical-twin pairs and 17 fraternal-twin pairs were studied. It
was found that of the 15 identical-twin pairs, 10 pairs had two
criminals while the remaining pairs had one criminal. Of the 17
fraternal-twin pairs, five pairs had two criminals, while the remain-
ing pairs had one criminal. Construct a contingency table for these
data. Test whether the two variables are independent using a
chi-square test. (Based on Guilford, 1965.)
4 A media lecturer is interested in the impact of viewing a Woody
Allen comedy on the mood of the viewers. He hypothesizes that the
mood of the viewers will be different after viewing the film. He uses
the measure of mood on which high scores indicate positive mood.
The score of the 10 participating viewers are recorded below:
Before: 12 16 17 10 18 16 15 11 12 15
After: 15 16 17 13 16 17 16 13 13 16
What statistical test would you use to test the researcher's hypo-
thesis? Perform the test and interpret the results.
5 You will need to carry out this exercise with the assistance of your
teacher and some very obliging colleagues. For each of 10 fellow
students, measure their head circumference in centimetres (or
inches) and the length of their foot (in cm or inches). Use SPSS or
Excel to find the correlation between head circumference and length
of foot. Interpret your findings.
6 Use the Rawstorne's computer anxiety data to find whether males
and females differ on the variable `confid1' ± confidence using com-
puters. High scores on this variable mean greater confidence. State
which test you would use and why. Use SPSS or Excel to conduct
the analysis.
7 Ask 10 of your fellow male students and 10 of your fellow female
students whether they prefer rock, jazz or classical music. They
must choose only one category. Construct the contingency table.
Are the two variables related or independent?
226

REFERENCES
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Erlbaum Associates.
Agrest, A (1990) Categorical Data Analysis. New York: Wiley.
Baller, W.R. (1936) `A study of the present states of adults who were mentally
deficient', Genetic Psychology Monography 18: 165±244.
Bishop, Y.M.M, Fienberg, S.E. and Holland, P.W. (1975) Discrete Multivarite Analysis.
Cambridge, MA: The MIT Press.
Burt, C. (1955) `The evidence for the concept of intelligence', British Journal of
Educational Psychology, 25: 158±77.
Burt, C. (1966). `The genetic determination of differences in intelligence: a study of
monozygotic twins reared together and apart', British Journal of Psychology, 57:
137±53.
Cohen, J. and Cohen P. (1983) Applied Multiple Regression and Correlation Analysis for
the Behavioural Sciences. Hillsdale, NJ: Lawrence Erlbaum Associates.
Draper, N.R. and Smith, H. (1981) Applied Regression Analysis. New York: John Wiley
and Sons.
Durkheim, E. (1964) The Rules of Sociological Methods. New York: Free Press.
Durkheim, E. (1970) Suicide: a study in sociology. London: Routledge and Kegan
Paul.
Edgington, E.S. (1964) `Randomization tests', Journal of Psychology, 57: 445±9.
Edgington, E.S. (1995) Randomization Tests. New York: Marcel Dekker.
Ferguson, G.A. (1959) Statistical Analysis in Psychology and Education. New York:
McGraw-Hill.
Guilford, J.P. (1954) Psychometric Methods. New York: McGraw-Hill.
Guilford, J.P. (1965) Fundamental Statistics in Psychology and Education. New York:
McGraw-Hill.
Hankins, F.H. (1968) Adolphe Quetelet as Statistician. New York: AMS Press.
Hayes, A.F. (1988) `SPSS procedures for randomization tests', Behavior Research,
Methods', Instruments and Computers, 30(3): 536±43.
Howell, D.C. (1992) Statistical Methods for Psychology. Belmont CA: Duxbury.
Innes, J.M. (1965) `A case study of problem solving', Bulletin of the British
Psychological Society, 18(61): 11±15.
Kamin, L. (1974) The Science and Politics of IQ. Hillsdale NJ: Erlbaum.
Kerlinger, F.N. and Pedhazur, E.J. (1973) Multiple Regression in Behavioral Research.
New York: Holt, Rinehart and Winston.
May, R.B. and Hunter, M. (1993) `Some advantages of permutation tests', Canadian
Psychology, 34: 401±7.
Manly, B.F.J. (1991) Randomization and Monte Carlo Methods in Biology. London:
Chapman and Hall.
Micceri, T. (1989) `The unicorn, the normal curve, and other improbable creatures',
Psychological Bulletin, 105: 156±66.
Moore, D.S. and McCabe, G.P. (1993) Introduction to the Practice of Statistics. New
York: Freeman.
Spearman, C. (1927/1932) The Abilities of Man. London: Macmillan.
Queen, E. (1983) The Dutch Shoe Mystery. London: Hamlyn.
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US Surgeon General (1964) Smoking and health. Report to the Advisory Committee to
the Surgeon General of the Public Health Service. Washington, DC: US Government
Printing Office.
Yule, G.U. and Kendall, M.G. (1937) An Introduction to the Theory of Statistics. London:
Charles Griffin.
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7
Summarizing and Presenting Results
`Quite so!'
`You see, Lady Swaffham, if ever you want to commit a murder, the thing you've got to
do is to prevent people from associatin' their ideas. Most people don't associate anythin' ±
their ideas just roll about like so many dry peas on a tray, makin' a lot of noise an' goin'
nowhere, but once you begin lettin' em string their peas into a necklace, it's goin' to be
strong enough to hang you, what?'
`Dear me!' said Mrs Tommy Frayle, with a little scream, `what a blessing it is none of my
friends have any ideas at all!'
`Y'see,' said Lord Peter, balancing a piece of duck on his fork and frowning, `it's only in
Sherlock Holmes and stories like that, that people think things out logically. Or'nar'ly, if
somebody tells you somethin' out of the way, you just say, `By Jove!' or `How sad!' an'
leave it at that, an' half the time you forget about it, `nless somethin' turns up afterwards to
drive it home.' (Sayers, 1989: 118)
Lord Peter Wimsey
Whose Body?
Associatin' ideas is what quantitative research is about. Good research
design and good data analysis assist in the process of associating ideas
and coming to a conclusion. But we are not ended there. Research also
has to be presented to readers ± to an audience. Those readers and that
audience have to be able to understand your research. Often research is not
only for the immediate experts in your field but for a broader public,
including policy makers and managers. If they cannot understand your
work, and make the associations that you expect, then your good design
and good analysis will be wasted.
The theme of this book has been detection and reasoning about evidence.
The different styles of reasoning about evidence in detective fiction ± deduc-
tion, induction, abduction ± have their counterpart in social science and in
statistics. But detectives like Sherlock Holmes sometimes mistake their
guesses for deductions. Holmes `meta-bets' ± he constructs scenarios
about real-world events that may or may not match up with those events.
Detectives bet by meta-abduction, social scientists also test their abductions.
Inspector Wexford was not impressed by Sherlock Holmes's methods, as
Burden recalls in Simisola:
Burden thought of something Wexford had once said to him about Sherlock
Holmes, how you couldn't solve much by his methods. A pair of slippers with
singed soles no more showed that their wearer had been suffering from a severe
chill than that he had merely had cold feet. Nor could you deduce from a man's

staring at a portrait on the wall that he was dwelling on the life and career of that
portrait's subject, for he might equally be thinking of how it resembled his
brother-in-law or was badly painted or needed cleaning. With human nature
you could only guess ± and try to guess right. (Rendell, 1994: 130)
Traditional ideas about `deduction' raise traditional debates about `laws' in
social science. Holmes, for example, assumes that from a small set of facts
he can deduce the whole chain of events, because he believes that events
exist in law-like causal chains: `all life is a great chain, the nature of which is
known whenever we are shown a single link' (Study in Scarlet). This `great
chain', however, may be closer to the idea of order at all points, introduced
in Chapter 1, rather than sets of laws to which we can refer our evidence.
The great chain of society and culture ± order at all points ± is created by
people and not by immutable unchangeable universal laws that govern
society and culture.
Qualitative and quantitative research exist on a continuum. Ql and Qt
researchers exist on a continuum and not as strict alternatives. Ql-oriented
researchers will often find themselves needing to use statistical models and
their ensuing graphic representations or software analysis programs that
allow representation of data in categorical form. Qt-oriented researchers
will find that they cannot help but preserve in their results the cultural
order that the statistics attempt to measure.
The case studies that we have presented in the previous chapters are
all examples of the qualitative and quantitative continuum. Hoftstede's
research on intercultural communication variables like individualism,
uncertainty avoidance, masculinity and power distance was deductive
and nomothetic. Hofstede acknowledged the idiographic when he took
into account the use of constructs in everyday life. He tried to to find
observable phenomena from which the constructs of everyday life can be
inferred (1984: 17).
Lazarsfeld's longitudinal study of the attitudes and behaviour of a panel
of voters during a United States presidential campaign, in contrast, was
inductive and nomothetic. He and his colleagues knew what they wanted
to study, but they did not have a highly structured theoretical approach
that determined the operationalization of their variables. In both cases,
Hoftstede's and Lazarsfeld's, however, care was taken with frame of
reference ± the cultural and language contexts to which operational
definitions, and questions, apply. Lazarsfeld's early triangulation of
methods, his combining of the qualitative and the quantitative is a good
example of an attempt at methods level to deal with order at all points:
1 Any phenomenon should be measured with objective observations as
well as with introspective reports.
2 Case studies should be combined with statistical information.
3 Data gathering should be combined with information about the history
of what is being studied.
230

4 Data from unobtrusive studies (e.g. observation) should be combined
with questionnaire and other self-reported data. (cited Rogers, 1994: 285)
Methodologies can be deductive and inductive in quantitative research.
Deduction, as a style of reasoning, certainly occurs in social science. But,
like induction and abduction, it is closer to the `probable' and `possible'
rather than the `necessary', and if it is the `necessary' then it is closer to C.S.
Peirce's examples presented in Chapter 3 than it is to traditional science:
I once landed at a seaport in a Turkish province; and as I was walking up to the
house which I was to visit, I met a man upon horseback, surrounded by four
horsemen holding a canopy over his head. As the governor of the province was
the only personage I could think of who would be so greatly honored, I inferred
that this was he. This was an hypothesis. (cited in Eco, 1983: 219)
This is a case of inferences based on conventions, not laws. All the case
studies that we have presented to you raise the problem of methodology,
hypothesis, research questions, identification and operationalization of con-
structs, measurement and judgements ± inferences ± about the results. The
research designs themselves can be deductive ± like those of Hofstede, or
inductive ± like those of Lazarsfeld. In the former, the research design has
formalized hypotheses that are to be tested ± there is less room for explora-
tion. In the latter research design, there are research questions and more
room for exploration. There can also be different degrees of nomotheticity in
different research designs. The big `nomothetic' studies seek answers to the
very big picture, such as Accounting for Tastes (1999), presented in Chapter 5,
which sought to answer questions about the relationship between social
class and culture and did so by quantifying social class and relating it to
cultural preferences.
It might be argued that we have not presented research examples that
used abduction, or guessing. However, not surprisingly, there is an element
of guessing in the whole process of a research project. Indeed, abduction is
involved in the very formation of a hypothesis as `an act of insight', the
`abductive suggestion' coming to us `like a flash' (cited in Sebeok and
Umiker-Sebeok, 1983: 18). Abduction is often the first step of social scientific
reasoning.
The idea of `guessing' and the idea of `mistake' also go hand in hand. A
guess can be wrong. A good research design and good data analysis reduce
the chances of bias and error. As we have seen, bias and error can happen in
many ways. They can happen with the styles of reasoning themselves, for
example mistaking ideology for deduction (as in the case of Carl Jung).
Error and bias can also happen in the operational definitions of constructs,
the choice of measurement techniques, sampling, the wording of questions,
the administration of the data-collecting instrument, data analysis and in
the interpretation of results. A good social scientist, therefore, needs to be
both a detective and a statistical sleuth (data snooper).
SUM M A R I Z I N G A N D P R E S E N T I N G R E S U LT S
231

Openness and accountability and following the professional code of
ethics are intended as good protections against acceptance of assertions
and appeals to authority without presentation and testing of evidence.
Other researchers should be able to test your methodology and critique
your conclusions. Holmes and Lord Peter Wimsey continually berated the
police for poor methodology. They argued that, in comparison to the police,
they were not only exceptionally gifted individuals, but good methodolo-
gists ± `You know my method. It is founded upon the observation of trifles',
says Holmes (The Boscombe Valley Mystery).
Professional codes of ethics are provided by the professional associations
of the different disciplines of social science. The codes are sometimes made
available on the internet site of the association. For instance, Appendix II is
an example from the British Sociological Association internet site. The
British and American Psychological Societies and other professional
research groups outline their professional and ethics codes.
REPORTING EMPIRICAL RESEARCH
Detectives in detective fiction sometimes write reports. Many of them, of
course, are not statistical in nature, although they are deductive. Ellery
Queen, for example, often presents to the reader what he has written in
his notebook. Chief Inspector Maigret, the French inspector, also writes
down what he knows and what he plans to do:
1. Telegraph Rouen
2. Telegraph Niel's
3. Look at yard
4. Get information on Saint-Hilaire property
5. Finger-prints on knife
6. List of hotel visitors
7. Engineer's family Hotel du Commerce
8. People who left Sancerre Sunday the 26th
9. Announce reward, by town-crier, to anyone who met Gallet Saturday the 25th.
(Simeon, 1977: 23)
Keeping a record of observations, of course, is essential to detection. The
accumulation of evidence assists with the associatin' of ideas. The detec-
tive's final report is the narrative explaining what happened and who killed
whom. In the case of Maigret Stonewalled, Maigret finds that the person
assumed to have been murdered in fact committed suicide. The suicide
had fabricated his death to look like a murder. Maigret does not report
his findings to his superiors or the insurance company because of the tragic
circumstances surrounding the death and the possible consequence if he
released his findings. There was, therefore, an ethics element to what he did
with his findings. Was Maigret right? Read the story.
232

The case studies presented in this book are good examples of reporting
social scientific empirical research. There is a presentation of the problem,
a literature review, methodology, findings and a conclusion. The journal
articles that you will have read during the course of the review exercises
in this book also give you a good indication of the standard formats for
reporting quantitative research findings.
Table 2.3 provided an overview of the types of content that are addressed
in both the design and reporting of quantitative research. But this overview
is not complete. Most articles in social science journals begin with an
ABSTRACT, set off from the text of the article. An abstract is a summary
of the research findings and is normally about 150 words in length. The
abstract gives an overview of the purpose of the research, the methods,
results and conclusions. Many of the database searches in modern univer-
sity libraries are not full-text, but searches of words in abstracts.
The first section of an article is the INTRODUCTION. The introduction
may not appear as a heading, but it tells the reader the rationale for the
research, background to the research (previous studies) and normally ends
in a formal statement(s) of hypothesis(es). Some articles have sub-headings
such as BACKGROUND and LITERATURE REVIEW. As we saw in
Chapter 2 in the review of the studies in the sociology of journalism, a
literature review is not simply a rote recitation of what people said ± parrot
fashion ± but an evaluation and a synthesis of previous studies.
The METHOD section gives the reader the specific rules for replicating
your study. It contains detailed information about how the study was con-
ducted. It tells the reader who the participants or subjects of the study were,
the procedures (a common sub-heading) that were used to conduct the
study, how variables were operationally defined, and which measures
were used (a common sub-heading).
The RESULTS section provides readers with a summary of the findings of
the research. It is here that the main findings relevant to the hypothesis or
hypotheses are presented and, in some cases, additional information as
well. It is in the results that the reader will encounter the relevant statistical
notation, tables and graphs. Table 7.1, taken from Accounting for Tastes,
TABLE 7.1 Example from Accounting for Tastes: combined music genre preferences by gender
Genres with no gender differences `Female'genres `Male'genres
Classical Light classical *** Heavy metal***
Avant-garde Musicals*** Rock**
Traditional jazz Religious*** Blues**
Modern jazz Easy listening*** Alternative rock**
Big band Top 40** Folk**
Soul* Techno**
Opera* CountryandWestern*
* p 0:1; **p 0:001; *** p 0:0001.
233

discussed in Chapter 5, is an example of tabular results and notation. The
table is derived from the combined preferences for music types and shows
those music genres for which there is no difference between males and
females in their musical preferences and those that are more likely to be
favoured by either males or females.
Notice that the p-value is stated clearly and simply at the bottom of
the table, although in this case the chi-square values and degrees of freedom
are not shown (indeed the type of statistic used is not stated in the text). The
data, though, is clearly categorical in nature.
Many of the statistics in the reporting of empirical results are presented as
p-values. If you are reading research results and there is no background
statistic, then it is best to ignore the values for statistics such as t, r,
chi-square, and so on, and look for p. If you are writing the research,
then it is useful to provide the background statistic for the reader's in-
formation.
In Table 7.1 the p-values have an asterisk. This shows that the associations
are significant. If the p-value is less than 0.01, it means that the probability
of the result occurring by chance is less than 10 per cent (behavioural
research often sets the minimum at 0.05, less than 5 per cent). If the p-
value is less than 0.001, then the probability of the result occurring by
chance is less than one-tenth of 1 per cent, and so on.
The results section of a report sometimes combines description of results
and detailed analysis, as in the case of Accounting for Tastes. However,
detailed analysis is often left for a separate DISCUSSION section. The dis-
cussion section presents the implications of the research and the extent to
which the hypotheses of the research were supported by the data. Indeed,
the author evaluates alternative explanations for the data and limitations
that might have been imposed or the study or problems that might have
emerged.
A CONCLUSION or SUMMARY, like the abstract, brings together for the
reader all the strands of the report. It includes all the significant information
about methods, findings and discussion.
Writing Style, Narrative Style
A report, essay, article or thesis describing the empirical results of a research
study requires a writing style, a narrative skill, which achieves a high level
of readability. You will find conventions and strategies for writing in a
range of resources (Anderson and Poole, 1994; Peters, 1985).
As a rule of thumb: (1) avoid colloquial, conversational and subjective
modes of expression and (2) avoid abbreviations such as and don't.
`Scientific writing is not of a personal or conversational nature and for
this reason the third person is commonly used. As a general rule, personal
pronouns such as I, we, you, me, my, our and us should not appear, except
in quotations' (Anderson and Poole, 1994: 6).
234

The `third person' rule holds in most cases. But sometimes the narrative
style may require the more personal touch. Social science projects, for
example, may use a methodology that requires the researcher to report
their own subjective experiences ± especially where they have been par-
ticipant observers.
Good research work can be marred by bad reporting; `proper presenta-
tion is an integral part of the whole project' (Anderson and Poole, 1994: 6).
You will, no doubt, develop your own style for reporting results and
arguing your case. But, whatever your style, your presentation should
ensure that:
1 people will understand and accept the evidence in the form you have
provided it;
2 the evidence is instrumental in making the case or in supporting the
claim;
3 the evidence is at an appropriate technical and intellectual level for the
proposed readers;
4 the readers know and respect the sources of evidence.
Detection and Deception
The problems you face in developing a narrative for your results are in
many ways no different from those faced by detectives in detective fiction.
You have to show that you understand your methods and that your reason-
ing about your results is sound. Detectives need tools, methods, to collect
their data. They are creative problem-solvers who know that it is important
to understand the reasoning behind their methods. Detectives make judge-
ments about individual pieces of evidence that may or may not be signs of
what really happened. Holmes and Lord Peter Wimsey were angry with
police detectives precisely because they believed that the police methods
did not yield real signs, real clues.
A social scientist often has to be a good detective and a good statistical
sleuth. Social scientists confront the general and the particular, the macro
and the micro, in theory and in practice. For example, theoreticians like
Durkheim used rates of suicide, a general classification, to show how
society regulates and integrates its members. In doing so he lost informa-
tion, especially information about the circumstances that underpinned the
classification of the `suicide' act itself.
But even when we are confident that our constructs measure what we say
they measure, we have to be careful with the statistical measures that we
choose. There are, as you have seen, quite complex statistical measures for
interpreting and summarizing individual scores, or values, that are
obtained from a study. Equations have definition, like any other construct,
and need to be carefully understood before they are used. They are general
classifications that can either enhance or obscure the real meaning of the
data that you are analysing.
235

This text is only an introduction to methods and basic statistics. Some of
the theory and methods look and are complex. Some of the statistics are
complex. But, as Sherlock Holmes says, `Come, the game is afoot!'
REFERENCES
Anderson, J. and Poole, M. (1994) Thesis and Assignment Writing. Brisbane: John
Wiley and Sons.
Bennett, T., Emmison, M. and Frow, J. (1999) Accounting for Tastes: Australian
Everyday Culture. Cambridge: Cambridge University Press.
Doubleday.
Eco, U. (1983) `Horns, hooves, insteps', in U. Eco and T. Sebeok (eds), The Sign of
Three: Dupin, Holmes, Pierce. Bloomington, IN: Indiana University Press.
Hofstede, G. (1984) Culture's Consequences: International differences in work-related
values. Beverley Hills, CA: Sage.
Peters, P. (1985) Strategies for Student Writers. Brisbane: John Wiley and Sons.
Rendell, R. (1994) Simisola. London: Random House.
Rogers, E.M. (1994) A History of Communication Study. New York: Free Press.
Sayers, D. (1989) Whose Body? Sevenoaks: New English Library.
Sebeok, T.A. and Umiker-Sebeok, J. (1983) `You know my method', in U. Eco and T.
Sebeok (eds), The Sign of Three: Dupin, Holmes, Pierce. Bloomington, IN: Indiana
University Press.
Simeon, G. (1977) Maigret Stonewalled. Harmondsworth: Penguin.
236

Appendix I
Sample Letter for Informed Consent
School/Division Title Murdoch University logo as per standard
letterhead
Project Title: Adult Literacy in Australia.
I am a (PhD/Honours/fourth year Psychology) student (member of staff) at
Murdoch University investigating the level of literacy among adults in Australia.
The purpose of this study is to find out what causes low levels of literacy among
some adults in Australia and to investigate how levels of literacy in Australia can be
improved.
You can help in this study by consenting to complete a survey. The time to
complete the survey will vary, however, it is anticipated that no more than two
hours will be necessary. Contained in the survey are questions about level of
education, income, and other questions which may be seen as personal and private.
Therefore, participants can decide to withdraw their consent at any time. All
information given during the survey is confidential and no names or other informa-
tion which might identify you will be used in any publication arising from the
research.
If you are willing to participate in this study, could you please complete the details
below. If you have any questions about this project please feel free to contact either
myself (investigator's name), on 9234 5678 or my supervisor, Dr John Smith, on 9360
2345.
My supervisor and I are happy to discuss with you any concerns you may have on
how this study has been conducted, or alternatively you can contact Murdoch
University's Human Research Ethics Committee on 9360 6677.
***********************************************************
I (the participant) have read the information above. Any questions I have asked have
been answered to my satisfaction. I agree to take part in this activity, however, I
know that I may change my mind and stop at any time (where applicable add ±
without prejudice to my future medical treatment).
I understand that all information provided is treated as confidential and will not be
released by the investigator unless required to do so by law.

I agree that research data gathered for this study may be published provided my
name or other information which might identify me is not used.
Participant/Authorised Representative:
Date:
Investigator:
Date:
Investigator's Name:
238

Appendix II
BSA Statement of Ethical Practice
The British Sociological Association gratefully acknowledges the use made of the
ethical codes produced by the American Sociological Association, the Association
of Social Anthropologists of the Commonwealth and the Social Research
Association.
Styles of sociological work are diverse and subject to change, not least because
sociologists work within a wide variety of settings. Sociologists, in carrying out
their work, inevitably face ethical, and sometimes legal, dilemmas which arise out
of competing obligations and conflicts of interest. The following statement aims to
alert the members of the Association to issues that raise ethical concerns and to
indicate potential problems and conflicts of interest that might arise in the course
of their professional activities.
While they are not exhaustive, the statement points to a set of obligations to
which members should normally adhere as principles for guiding their conduct.
Departures from the principles should be the result of deliberation and not ignor-
ance. The strength of this statement and its binding force rest ultimately on active
discussion, reflection, and continued use by sociologists. In addition, the state-
ment will help to communicate the professional position of sociologists to others,
especially those involved in or affected by the activities of sociologists.
The statement is meant, primarily, to inform members' ethical judgements
rather than to impose on them an external set of standards. The purpose is to
make members aware of the ethical issues that may arise in their work, and to
encourage them to educate themselves and their colleagues to behave ethically.
The statement does not, therefore, provide a set of recipes for resolving ethical
choices or dilemmas, but recognises that often it will be necessary to make such
choices on the basis of principles and values, and the (often conflicting) interests
of those involved.
PROFESSIONAL INTEGRITY
Members should strive to maintain the integrity of sociological enquiry as a dis-
cipline, the freedom to research and study, and to publish and promote the results
of sociological research. Members have a responsibility both to safeguard the
proper interests of those involved in or affected by their work, and to report
their findings accurately and truthfully. They need to consider the effects of
their involvements and the consequences of their work or its misuse for those
they study and other interested parties.
While recognising that training and skill are necessary to the conduct of social
research, members should themselves recognise the boundaries of their profes-
sional competence. They should not accept work of a kind that they are not
qualified to carry out. Members should satisfy themselves that the research they

undertake is worthwhile and that the techniques proposed are appropriate. They
should be clear about the limits of their detachment from and involvement in their
areas of study.
Members should be careful not to claim an expertise in areas outside those that
would be recognised academically as their true fields of expertise. Particularly in
their relations with the media, members should have regard for the reputation of
the discipline and refrain from offering expert commentaries in a form that would
appear to give credence to material which, as researchers, they would regard as
comprising inadequate or tendentious evidence.
RELATIONS WITH AND RESPONSIBILITIES TOWARDS RESEARCH
PARTICIPANTS
Sociologists, when they carry out research, enter into personal and moral relation-
ships with those they study, be they individuals, households, social groups or
corporate entities. Although sociologists, like other researchers are committed to
the advancement of knowledge, that goal does not, of itself, provide an entitle-
ment to override the rights of others. Members must satisfy themselves that a
study is necessary for the furtherance of knowledge before embarking upon it.
Members should be aware that they have some responsibility for the use to which
their research may be put. Discharging that responsibility may on occasion be
difficult, especially in situations of social conflict, competing social interests or
where there is unanticipated misuse of the research by third parties.
1. Relationships with research participants
. Sociologists have a responsibility to ensure that the physical, social and
psychological well-being of research participants is not adversely affected
by the research. They should strive to protect the rights of those they study,
their interests, sensitivities and privacy, while recognising the difficulty of
balancing potentially conflicting interests. Because sociologists study the
relatively powerless as well as those more powerful than themselves,
research relationships are frequently characterised by disparities of power
and status. Despite this, research relationships should be characterised,
whenever possible, by trust. In some cases, where the public interest dic-
tates otherwise and particularly where power is being abused, obligations
of trust and protection may weigh less heavily. Nevertheless, these obliga-
tions should not be discarded lightly.
. As far as possible sociological research should be based on the freely given
informed consent of those studied. This implies a responsibility on the
sociologist to explain as fully as possible, and in terms meaningful to par-
ticipants, what the research is about, who is undertaking and financing it,
why it is being undertaken, and how it is to be promoted.
. (i) Research participants should be made aware of their right to refuse
participation whenever and for whatever reason they wish.
. (ii) Research participants should understand how far they will be
afforded anonymity and confidentiality and should be able to reject
the use of data-gathering devices such as tape recorders and video
cameras. Sociologists should be careful, on the one hand, not to give
240

unrealistic guarantees of confidentiality and, on the other, not to permit
communication of research films or records to audiences other than
those to which the research participants have agreed.
. (iii) Where there is a likelihood that data may be shared with other
researchers, the potential uses to which the data might be put may
need to be discussed with research participants.
. (iv) When making notes, filming or recording for research purposes,
sociologists should make clear to research participants the purpose of
the notes, filming or recording, and, as precisely as possible, to whom it
will be communicated.
. (v) It should also be borne in mind that in some research contexts,
especially those involving field research, it may be necessary for the
obtaining of consent to be regarded, not as a once-and-for-all prior
event, but as a process, subject to renegotiation over time. In addition,
particular care may need to be taken during periods of prolonged field-
work where it is easy for research participants to forget that they are
being studied.
. (vi) In some situations access to a research setting is gained via a `gate-
keeper'. In these situations members should adhere to the principle of
obtaining informed consent directly from the research participants to
whom access is required, while at the same time taking account of
the gatekeeper's interest. Since the relationship between the research
participant and the gatekeeper may continue long after the sociologist
has left the research setting, care should be taken not to disturb that
relationship unduly.
. It is incumbent upon members to be aware of the possible consequences of
their work. Wherever possible they should attempt to anticipate, and to
guard against, consequences for research participants which can be pre-
dicted to be harmful. Members are not absolved from this responsibility
by the consent given by research participants.
. In many of its guises, social research intrudes into the lives of those studied.
While some participants in sociological research may find the experience a
positive and welcome one, for others, the experience may be disturbing.
Even if not exposed to harm, those studied may feel wronged by aspects of
the research process. This can be particularly so if they perceive apparent
intrusions into their private and personal worlds, or where research gives
rise to false hopes, uncalled for self-knowledge, or unnecessary anxiety.
Members should consider carefully the possibility that the research experi-
ence may be a disturbing one and, normally, should attempt to minimise
disturbance to those participating in research. It should be borne in mind
that decisions made on the basis of research may have effects on individuals
as members of a group, even if individual research participants are pro-
tected by confidentiality and anonymity.
. Special care should be taken where research participants are particularly
vulnerable by virtue of factors such as age, social status and powerlessness.
Where research participants are ill or too young or too old to participate,
proxies may need to be used in order to gather data. In these situations care
should be taken not to intrude on the personal space of the person to whom
the data ultimately refer, or to disturb the relationship between this person
and the proxy. Where it can be inferred that the person about whom data
B S A S TAT E ME N T O F E T HI C A L P R AC T I C E
241

are sought would object to supplying certain kinds of information, that
material should not be sought from the proxy.
2. Covert research
There are serious ethical dangers in the use of covert research but covert methods
may avoid certain problems. For instance, difficulties arise when research parti-
cipants change their behaviour because they know they are being studied.
Researchers may also face problems when access to spheres of social life is closed
to social scientists by powerful or secretive interests. However, covert methods
violate the principles of informed consent and may invade the privacy of those
being studied. Participant or non-participant observation in non-public spaces or
experimental manipulation of research participants without their knowledge
should be resorted to only where it is impossible to use other methods to obtain
essential data. In such studies it is important to safeguard the anonymity of
research participants. Ideally, where informed consent has not been obtained
prior to the research it should be obtained post-hoc.
3. Anonymity, privacy and confidentiality
1. The anonymity and privacy of those who participate in the research process
should be respected. Personal information concerning research participants
should be kept confidential. In some cases it may be necessary to decide
whether it is proper or appropriate even to record certain kinds of sensitive
information.
2. Where possible, threats to the confidentiality and anonymity of research
data should be anticipated by researchers. The identities and research
records of those participating in research should be kept confidential
whether or not an explicit pledge of confidentiality has been given.
Appropriate measures should be taken to store research data in a secure
manner. Members should have regard to their obligations under the Data
Protection Act. Where appropriate and practicable, methods for preserving
the privacy of data should be used. These may include the removal of
identifiers, the use of pseudonyms and other technical means for breaking
the link between data and identifiable individuals such as `broadbanding' or
micro-aggregation. Members should also take care to prevent data being
published or released in a form which would permit the actual or potential
identification of research participants. Potential informants and research
participants, especially those possessing a combination of attributes which
make them readily identifiable, may need to be reminded that it can be
difficult to disguise their identity without introducing an unacceptably
large measure of distortion into the data.
3. Guarantees of confidentiality and anonymity given to research participants
must be honoured, unless there are clear and overriding reasons to do
otherwise. Other people, such as colleagues, research staff or others, given
access to the data must also be made aware of their obligations in this
respect. By the same token, sociologists should respect the efforts taken
by other researchers to maintain anonymity. Research data given in con-
fidence do not enjoy legal privilege, that is they may be liable to subpoena
by a court. Research participants may also need to be made aware that it
may not be possible to avoid legal threats to the privacy of the data.
242

4. There may be less compelling grounds for extending guarantees of privacy
or confidentiality to public organisations, collectivities, governments, offi-
cials or agencies than to individuals or small groups. Nevertheless, where
guarantees have been given they should be honoured, unless there are clear
and compelling reasons not to do so.
4. Reputation of the Discipline
During their research members should avoid, where they can, actions which
may have deleterious consequences for sociologists who come after them or
which might undermine the reputation of sociology as a discipline.
RELATIONS WITH AND RESPONSIBILITIES TOWARDS SPONSORS
AND/OR FUNDERS
A common interest exists between sponsor, funder and sociologist as long as the
aim of the social inquiry is to advance knowledge, although such knowledge may
only be of limited benefit to the sponsor and the funder. That relationship is best
served if the atmosphere is conducive to high professional standards. Members
should attempt to ensure that sponsors and/or funders appreciate the obligations
that sociologists have not only to them, but also to society at large, research
participants and professional colleagues and the sociological community. The
relationship between sponsors or funders and social researchers should be such
as to enable social inquiry to be undertaken as objectively as possible. Research
should be undertaken with a view to providing information or explanation rather
than being constrained to reach particular conclusions or prescribe particular
courses of action.
1. Clarifying obligations, roles and rights
. Members should clarify in advance the respective obligations of funders
and researchers where possible in the form of a written contract. They
should refer the sponsor or funder to the relevant parts of the professional
code to which they adhere. Members should also be careful not to promise
or imply acceptance of conditions which are contrary to their professional
ethics or competing commitments. Where some or all of those involved in
the research are also acting as sponsors and/or funders of research the
potential for conflict between the different roles and interests should also
be made clear to them.
. Members should also recognise their own general or specific obligations to
the sponsors whether contractually defined or only the subject of informal
and often unwritten agreements. They should be honest and candid about
their qualifications and expertise, the limitations, advantages and disadvan-
tages of the various methods of analysis and data, and acknowledge the
necessity for discretion with confidential information obtained from spon-
sors. They should also try not to conceal factors which are likely to affect
satisfactory conditions or the completion of a proposed research project or
contract.
243

2. Pre-empting outcomes and negotiations about research
. Members should not accept contractual conditions that are contingent upon
a particular outcome or set of findings from a proposed inquiry. A conflict
of obligations may also occur if the funder requires particular methods to
be used.
. Members should try to clarify, before signing the contract, that they are
entitled to be able to disclose the source of their funds, its personnel, the
aims of the institution, and the purposes of the project.
. Members should also try to clarify their right to publish and spread the
results of their research.
. Members have an obligation to ensure sponsors grasp the implications of
the choice between alternative research methods.
3. Guarding privileged information and negotiating problematic sponsorship
. Members are frequently furnished with information by the funder who may
legitimately require it to be kept confidential. Methods and procedures that
have been utilised to produce published data should not, however, be kept
confidential unless otherwise agreed.
. When negotiating sponsorships members should be aware of the require-
ments of the law with respect to the ownership of and rights of access
to data.
. In some political, social and cultural contexts some sources of funding and
sponsorship may be contentious. Candour and frankness about the source
of funding may create problems of access or co-operation for the social
researcher but concealment may have serious consequences for colleagues,
the discipline and research participants. The emphasis should be on max-
imum openness.
. Where sponsors and funders also act directly or indirectly as gatekeepers
and control access to participants, researchers should not devolve their
responsibility to protect the participants' interests onto the gatekeeper.
Members should be wary of inadvertently disturbing the relationship
between participants and gatekeepers since that will continue long after
the researcher has left.
4. Obligations to sponsors and/or Funders During the Research Process
. Members have a responsibility to notify the sponsor and/or funder of any
proposed departure from the terms of reference of the proposed change in
the nature of the contracted research.
. A research study should not be undertaken on the basis of resources known
from the start to be inadequate, whether the work is of a sociological or
inter-disciplinary kind.
. When financial support or sponsorship has been accepted, members must
make every reasonable effort to complete the proposed research on sched-
ule, including reports to the funding source.
. Members should be prepared to take comments from sponsors or funders
or research participants.
. Members should, wherever possible, spread their research findings.
. Members should normally avoid restrictions on their freedom to publish or
otherwise broadcast research findings.
244

At its meeting in July 1994, the BSA Executive Committee approved a set of Rules for the
Conduct of Enquiries into Complaints against BSA members under the auspices of this
Statement, and also under the auspices of the BSA Guidelines on Professional Conduct. If
you would like more details about the Rules, you should contact the BSA Office at the
address/phone number given at the end of this statement.
British Sociological Association, Units 3F/G, Mountjoy Research Centre, Stockton
Road, DURHAM, DH1 3UR [UK]. Tel.: [+44](0)191 383 0839; fax: [+44](0)191 383
0782; e-mail: enquiries@britsoc.org.uk
245

Appendix III
The Statistical Inquirer
The Statistical Inquirer is designed to assist you in learning basic statistics. There are
five main activities available on the CD-R:
1 Research Files
2 Visual tutorials (video lessons on SPSS)
3 An Unsolved Mystery
4 A calculator (if you do not own one)
5 A real dataset from a study on computers and behaviour.
The answers to the lessons and to the mystery are not provided in the book or the
CD±R ± you will have to work them out yourself!
MINIMUM SYSTEM REQUIREMENTS
Macintosh 1 PowerPC or compatible
Systems software 8.1 (or later)
20MB RAM allocated
CDROM player
256 colour monitor capable of 800600 resolution
100MB hard disk space required
PC
Pentium class CPU
Microsoft Windows 95 (or later)
64MB system memory
CDROM player
INSTRUCTIONS
Macintosh
Double-click on the StatInquirer icon on your desk top. Transfer the StatInquirer
folder to your hard disk. Open the StatInquirer folder on the hard disk and double-
click on the StatInquirer icon.
The video lessons for SPSS are held on the CD±R in the Movies folder. You need to
have QuickTime installed on your machine. Double click on the movie that you want
to view.

PC
The CD±R should start automatically. If it does not, then go to the CD±R double click
on menu.exe.
RESEARCH FILES
The research files contain library and statistics lessons. They are step-by-step
lessons. If you make a mistake, then you may be given an alternative explanation
or asked to key in your answer again.
Library
. finding books and articles
. databases
. Boolean operators and/or/not
Order and classification
. defining variables
. continuous and discrete variables
. arrays
. class sizes and recorded limits
. frequency distributions
. statistical tables and graphs
. general theoretical curves
. histograms and polygons
. the normal curve
. skewness
Central tendencies
. measures of central tendency
. some notation
. computing the mean for grouped data
. frequency distribution tables
. two formulae for calculating the mean of a distribution
. finding the median of a distribution
. finding the mode of a distribution
Variability
. range
. resistant measures
. mean deviation
. some notation
. Mean Absolute Deviation (MAD)
. standard deviation
. variance
T HE S TAT I S T I C A L I N Q U I R E R
247

Relationships
. statistical estimation
. correlation
. causation
. scatterplots
. linear relationships
. size and magnitude of relationships
. Pearson Product Moment Correlation
. regression
Statistical Inference
. samples and populations
. probability and statistical inference
DATASET
A real dataset is available on the CD±R under the file name companxi.sav. This
dataset is used in the video lessons and is also available for practice in SPSS.
SPSS VIDEO LESSONS
The video lessons on SPSS are in QuickTime for Macintosh users and in Lotus
ScreenCam for PC users. The lessons provide a brief introductory to:
. how to create variables in SPSS
. summary statistics
. analysing categorical variables
. one sample t-tests and chi-square
. t-tests
. regression equations
. bivariate statistics (correlations and scatterplots)
. non-parametric statistics
UNSOLVED MYSTERY
Dr Ogle has gone missing. Your task is to find out what happened to him.
248

abduction (guessing) 36, 39, 50, 64, 231
in detective fiction 14, 59
undercoded and overcoded 37
Abelson, R.P. 110, 112, 114, 121±2, 218
The Abilities of Man 216
Accounting for Tastes: Australian Everyday
Culture 122±33, 231
SPSS dataset 124±31
Adams, Douglas 14±16
Adorno, Theodore 97
The Adventure of the Copper Beeches (Arthur
Conan Doyle) 109
advertising psychology 71±3
Agresti, A. 193
Aisbett, K. 22
American Psychological Society 232
American Sociological Association 239
analytic mentality 7, 8
Anderson, J. 234±5
anomy 222
appeal to authority 23±4
arithmetic mean see mean
Aronson, E. 74
assertions, unsupported 23
Association of Social Anthropologists of the
Commonwealth 239
Australian Everyday Cultures Project
(AECP) 123
Australian Institute of Industrial
Psychology 71
Australian Standard Classification of
Occupations (ASCO) 123
The Authoritarian Personality 97
average see central tendency; mean; median
Babbie, E. 16, 52, 85
back-to-back plots 112
background statistic, presenting 234
Baller, W.R. 191±3
Bancroft, G. 82
Baranek, Patricia 4
behaviour
actual and reported 20±1
and media violence 22±4
Bennett, T. 122, 123, 124
Benson and Oslick 171
Berelson, B. 97
between-subject (independent)
experimental design 74±5
bias
avoiding 65, 82
and error 81, 103, 231
social 49±50, 87, 222
Bills of Mortality 75±6
Bishop, Y.M.M. 171
bivariate data 149±63
categorical 171±5
plotting 149±51
The Blue Cross (G.K. Chesterton) 38
Bodiger, H. 75
body-builds, stereotypes 24±5
Bogardus, E.S., Social Distance scale 80
The Boscombe Valley Mystery (Arthur Conan
Doyle) 33, 109, 232
Bossner 216
Bottomore, T.B. 76
Bouma, G.D. 26
Bourdieu, Pierre 123
Bowman, W.W. 17
boxplots 115±18, 129±30
Boyd-Barrett, Oliver 19±20
Braverman, J. 71
British Psychological Society 232
British Sociological Association 232, 239±45
Brown, Father 10±13, 16, 27, 38
Burgess, R.G. 95
Burt, Sir Cyril 217±18
bystander apathy 75
Cadfael, Brother 64
Cannell, C. 81±2, 87
Caputi, P. 112
carry over effects 90
case studies 25, 66, 230
categorical data
bivariate 171±5
one-sample test 183±4
tests 191±3
Index

categorical data (cont.)
see also nominal measures
categories, unordered 47±8
causality
in detective fiction 10±16
diagram 42±4
establishing 23, 40±1, 59±60, 70±1, 103,
161±2
hypotheses 45
necessary and sufficient conditions
40±1
causation see causality
Cause of Death (Patricia Cornwell) 16±17
cause and effect see causality
censuses 26, 75, 76
central tendency 132, 133±4, 143
centrality see central tendency
Chambers, J.M. 110
Chan, Janet 4
Chandler, Raymond 44, 90
Chesterton, G.K. see Brown, Father
chi-square 172±4, 184, 199
Christie, Agatha 109
Christie, R. 80
clairvoyance testing, Pearce±Pratt studies
112
Cliff, N. 47
closure 16
Clouseau, Inspector 81
cluster sampling, multi-stage 92±3
coding of responses 85, 87
coefficient of determination 161
Cohen, J. 161
Cohen, P. 161
collective societies 55
Columbia University 96±7
Columbo (television detective) 68
Comte, August 40
Conan Doyle, Arthur see Holmes, Sherlock
confidence intervals 180, 181, 188, 189
confounding variables 162
consent, informed 237±8, 240
consistency, excessive 218
construct validity 89
contingency
coefficient 174±5
questions 84
tables 173
contrast error 81
control group 69, 98
Conway, J. 218
Cooke, Janet 18
correlated samples, rank test 195±6
correlation 70, 103, 151±7, 223±4
coefficient 152, 153, 154±5, 165, 214, 215
Excel 169±71
SPSS 163±8
correlational statements 44±5
cross-cultural studies 51±9
cross-sectional designs 26
cultural data, reliability 5±7
cultural values 53, 60, 123
cultural variation, measuring 51±9
Cumberbatch, G. 22±3
cumulative scales 80
curvilinear relationship 155
data
analysis 109±46
clustering 151
collection 65±7, 76, 230
description 132±42
entry 85, 151
error checking 151
fraudulent 110, 142
graphical presentation 110±22
interpretation 142
negative and positive associations 150
ordinal 48
qualitative 47±8
recognizing 64
reframing 121±2
reliability 5±7
secondary analysis 25
snooper, definition 110
in social sciences 30
summarizing 142
variable by case matrix 76
David, F.N. 76
Davis, A. 75, 90
Davis, J.A. 42
deception, and detection 235±6
decision-making 39
deduction 37, 231
DeFleur, M.L. 23
degrees of freedom 182, 184, 188
demographics 53
Denzin, Norman 95
detection, and deception 235±6
detective fiction 10±16, 27, 44
see also under names of fictional detectives
DeVaus, D.A. 82
diagrams, causal 41±4, 60
Dichter, Ernest 72, 73
differential scales 79±80
digital persona 76
Dillman, D.A. 85
Dirk Gently's Holistic Detective Agency 14±16
dispersion indices 143
I N D E X
250

disproportionate stratified random
sampling 92
distribution
central tendency 132
normal see normal distribution
shape 132
skewed 116, 138
distribution-free tests 189, 195
divine punishment 76
Dominick, J.R. 24
Doyle, A. Conan see Holmes, Sherlock
Draper, N.R. 161
Durkheim, Emile 40, 214, 218±23, 235
Durkin, K. 22
Eco, Umberto 36±7, 39, 44, 88, 103, 231
Edgington, E.S. 211, 213
Emmison, M. 122
equality of means, for independent samples
185±9
Ericson, Richard 4
errors 27, 81, 103, 160, 177, 231
estimation 157, 160, 176, 223
ethics 59, 70, 74, 232, 239±45
ethnography 52
ethnomethodology 8, 52
ethnoscience 52
evaluation of programmes 76
Everington, C. 24±5
evidence
definition 27
empirical 29
evaluation 147, 235
evolution 152, 214
Excel
chi-square tests 199
correlation analysis 169±71
data analysis 131±2
data description 140±2
data plotting 131±3
graphical presentations 3
one-sample tests 198±201
scatterplots 168±71
t-test 211
two-sample tests 204±8
experiment, Piagetian 90
between-subject (independent) 74±5
ex post facto 70
laboratory and field 75
types 74±5
validity 87±90
within-subjects 74±5, 193
exploratory data analysis 110
exploratory research 16±20
external and internal validity 22, 89, 90±6
Farquar, A.B. and H. 118
Father Brown see Brown, Father
Ferguson, G.A. 184
Fienberg, S.E. 171
figures see graphical presentation
Finch, S. 47
Fink, A. 78
five-number summary 116
five-point scale 47
Forrest, D.W. 215
Fortune survey 94
frame of reference 82±3, 230
fraud 110, 142, 218
frequencies, expected and observed 173, 192
frequency distribution 113±14
Friedlander, S. 49
Frow, J. 122
Gallup polls 94
Galton, Sir Francis 152, 153, 214±15
Garfinkel, Harold 5, 8
Gaudet, H. 97
Gauss 214
Geiss, F.L. 80
gender differences 54
generosity error 81
genetics 183±4, 214±15
Gently, Dirk 14±16
Gillie, Oliver 218
goal of study 24
The Good Life (television series) 74±5
Gossett, William (Student) 182
government agencies, questionnaire design
83
graphical presentation
aid to understanding 110
best practice 118±20
bivariate data 149±51
data 110±22
Excel spreadsheet 3
frequency distribution 113±14
limitations 142
misleading 120±2
guessing see abduction
Guilford, J.P. 191, 215
Hacking, I. 50
halo effect 81
Hamlet (Shakespeare) 67±8
Hansel, C.E.M. 113
Hawthorne experiments 71
Hayes, A.F. 213
I N D E X
251

Hempel, C.G. 39
Henningham, John 17
Hickson, D.J. 41
hierarchical ordering 216
hinge 115±16
histograms 113±15, 129
Ho, R. 119
Hofstede, Geert 51±9, 60, 76, 104, 230, 231
Holland, P.W. 171
Holmes, Sherlock
belief in causality 34±6, 44, 230
cases 25
deduction 13±14
evaluation of evidence 147, 148
guessing (abduction) 37, 50, 59
identification of individuals 21±2
importance of data 64
meta-betting 229
observation 33±4
poor opinion of police 27, 33±4, 232, 235
prejudice 27, 109
as problem-solver 147
l'homme moyen 214
The Hound of the Baskervilles (Arthur Conan
Doyle) 37
Hovland, Carl 73±4
Howard, Margaret 218
Howell, D.C. 193
Howitt, D. 22±3
Hunt, M. 94
Hunter, M. 212
hypotheses
causal 45, 60
correlational 44±5, 60
criteria 45
in detective fiction 44
operationalization 53±6
testing 27, 180, 212, 231
ideas, association 229
ideology 59, 231
idiographic model 16, 30, 52, 59, 98, 223
imagery training 185
independence, testing 208±10
independent samples 186±9
rank test 189±91
t-test 186
independent variables 42, 46, 53
individualism 55, 56
induction 231
industrial psychology 71
inference, statistical 33, 36, 93, 175±96
informed consent 237±8, 240
Innes, J.M. 148
insight 37, 39, 231
Institute of Motivational Research 72
instrument effects 90
intelligence
genetic component 217±18
quotient (IQ) 78
two-factor theory 215±17
internal validity 89, 90, 96, 103
interpretation, first and second order 5
interquartile range 136
interval-level measurement 47, 60, 78±9
interviewer bias 87
interviews 72, 85±7
introspective reports 230
intuition 37
inventory (test) 159
IQ tests 78, 191±3
item scales, bias/error 81
J. Walter Thomson (advertising company)
71±2
Johnstone, J.W.C. 17±18
journal articles, structure 233±4
journalists
characteristics 17±20
and units of analysis 21±2
Judd, C.M. 89
judgements 39, 95
Jung, Carl 49, 231
Kahn, R.L. 81±2, 87
Kalof, L. 23
Kamin, L. 218
Kaplan, R.M. 70
Kendall, M.G. 214
Kerlinger, F.N. 161
Kidder, L.H. 89
knowledge, required by respondents 83
Kosecoff, J. 78
Lady of the Lake (Raymond Chandler)
90±1
language, of questions 81±3
Laplace 214
Lazarsfeld, Paul 96±102, 103, 230, 231
least squares method 157±60
Lever (soap manufacturer) 72
Lichter, L.S. 18
Lichter, S.R. 18
Likert, R. 80
linear relationship 150, 155
Literary Digest polls 93±4
literature review 22±5, 30, 233
location see central tendency
log-linear models 193
I N D E X
252

logic 29, 34, 39
longitudinal research 25±7
Lovell, Tasman 71
Lowrey, S. 23
Lumsdaine, A.A. 73
lung cancer, and smoking 161±2
McCabe G.P. 186
Mach IV scale 80±1
McHoul, Alec 2, 8
McNeill, P. 29
McQuail, D. 101
Maigret, Chief Inspector 232
Maigret Stonewalled (Georges Simenon) 232
Manly, B.F.J. 213
Mann±Whitney, U test 189±91, 203
marginals 173
market segments 72
Marlowe, Philip 44, 90±1
Martin, A.H. 71
Marx, Karl 76
masculinity 55, 56
mass media see media
matched participants 193
mathematical notation 133±4, 143
mathematical possibilities, quantitative
analysis 48±50
maturation effects 90
maximum and minimum values 115
May, R.B. 212, 213
Mayo, Elton 71
mean
arithmetic 133
calculation 47
definition 133
equality, for independent samples 185±9
and median 134±5
sampling distribution 179
measurement 44±51
media
effects 2±4, 22±4, 100, 101
theory 96
see also journalists
median
calculating 47, 133±4
definition 115, 133±4
and mean 134±5
resistant measure 135
sampling distribution 179
Mendel, Gregor 183±4
Merril Carlsmith, J. 74
Merton, Robert 96
meta-abduction 229
meta-betting 36, 40, 50, 229
methodology 34±44, 52
Micceri, T. 224
Mickler, Steve 2
Milgram, Stanley 106
Mitchell, J. 50, 51
mode, as measure of location 134
Moore, D.S. 186
Moriarty, Professor 25
multinational company, employee morale
51
multiple-item scales 79±80
multi-stage cluster sampling 92±3
multivariate analysis 149
The Name of the Rose (Umberto Eco) 36, 88
narrative style 234±5
nature/nurture debate 215±18
Nazi Germany 49±50, 59, 97
negative and positive associations, data
150
news reporting see journalists; media
Newton, Isaac 147
Nightingale, Florence 76
nominal measures 46, 48, 60, 77±8
nomothetic measures 16, 30, 34, 52, 59, 98,
213, 223, 231
non-parametric tests 189, 195
non-probability sampling 95
normal distribution 138, 178, 179, 213±14
null hypothesis 180, 212
numbers, assigning to attributes 46
numerical summaries 132, 152
observations
analysis 33
indirect 75
objective 230
in quantitative research 33
and questionnaires 231
categorical data 183±4
Excel 198±201
SPSS 196±8
operational definitions 48±50
operationalization 53±6, 60
opinions, artificially created 83
opportunistic sampling 95
The Oracle of the Dog (G.K. Chesterton)
10±11
order
at all points 5, 230
effects 90
finding or imposing 213
inherent 6
of interpretation 5
I N D E X
253

ordinal level questions 46±7, 48, 60, 78
outliers 150, 151, 156, 160
p-value 180, 181, 195, 234
parameters, population 176
participant observation 65, 66
patterns, finding and interpreting 213
Pattison, P. 47
Pearce±Pratt studies, clairvoyance testing
112
Pearson, Sir Karl 152, 214
Pearson product moment correlation 152,
153, 165
Pedhazur, E.J. 161
The People's Choice 96±102, 103±4, 110
perceptions 53
personal goals and beliefs 53, 55
personal influence 101
Peters, Ellis 64
Peters, P. 234
Piagetian experiment 90
Piele, J. 28
Pierce, C.S. 37, 39, 231
pilot study 87
Pinckney Gag rule (1836) 171
placebo effect 69
planning of policy or programmes 76
plant breeding 183±4, 214±15
Poirot, Hercule 109
political behaviour 96±102
Poole, M. 234±5
population
analysis 153
definition 103
homogeneous or heterogeneous 93
parameters 176, 177
and sample 91, 176
positive association 150, 155
positivism 7
possibilities and probabilities 39
post-coding 78
power distance 56±7
Pratt, J.G. 112
prediction 152, 156±7, 223
presidential elections, forecasting 94, 230
Presser, Stanley 81
probability sampling 91, 92
product moment correlation, Pearson 152,
153
propaganda 73±4, 100
psychoanalysts, expertise 72
psychology, commercial applications 71±3
publications, structure 233±4
Pugh, D.S. 41
Q (Star Trek character) 7
qualitative data 47±8
qualitative (Ql) and quantitative (Qt)
methods 1±5, 8, 29, 230
quality control 182
quantitative research
association of ideas 229
data 47±8
mathematical possibilities 48±50
measuring attributes 51
observations 33
organizing 28
reliability 6
uses 7
see also qualitative (Ql) and quantitative
(Qt) methods
quartiles 115, 136
Queen, Ellery 41, 147±8, 232
questionnaires
accuracy of response 84, 85
administering 84
coding system 85
cost effective 103
design and layout 77, 83, 84±6, 88
and observation 231
response rate 85±6
standardized 51, 53
statistical analysis of results 77
survey 76
variable by case data matrix 67
questions
contingency 84
double-barrelled 82
interval-level 78±9
leading 82
negative 82±3
nominal level 77±8
open and closed 78
ordinal level 78
ratio level 79
wording 81±3
Quetelet, Adolphe 214
random number table 91, 92
random sampling 91, 92
randomization tests 211±13
range 135
rank order 77±8, 89
rank test
correlated or related samples 195±6
independent samples 189±91
Rapley, Mark 8
ratio-level measurement 47, 60, 79
Rawsthorne, Patrick 29, 112
reasoning, styles 36±40, 59
I N D E X
254

The Red-Headed League (Arthur Conan
Doyle) 148
regimes of value 123
regression 152
equation 158
line, finding 159±60
model, assessing the fit 160±1
multiple 162
simple linear 156±62, 214
SPSS 163±8
to the mean 152, 215
usefulness 162
related samples, tests 193±6
relationships, mapping 41±4, 60
reliability 6, 90
religion, and suicide 220
Rendell, Ruth 229±30
research
administrative 97
critical 97
design and methods 25, 27, 65, 66
exploratory 16±20
participants 240±3
replication 25
reporting 232±6
topic 16±21
The Resident Patient (Arthur Conan Doyle)
34±6
residuals 157, 160
resistant statistics 135, 156
response variables 156
results, presenting and summarizing 229±36
The Retired Colourman (Arthur Conan Doyle)
37
reversion 215
Rhine, J.B. 112
Roe, Phil 6
Rogers, E.M. 102
Rothman, S. 18
Rubel, M. 76
Rubin, A.M. 28
Rubin, R.B. 28
Sacks, Harvey 5±7, 8
samples/sampling
analysis 153
costs 93, 94
distributions 177±9, 185, 213
error 177
and external validity 90±6
frame 91, 103
independent 185, 186±9
judgement 95
multi-stage cluster 92±3
non-probability 95
opportunistic 95
and population 21, 176
related 193±5
reliability 6
simple random 91
size 93±4
snowball 95
statistics 176, 177
systematic 92
theoretical 95
types 94
unrepresentative 94
The Sanctuary Sparrow (Ellis Peters) 64
satisfactions 53
Sayers, Dorothy 64±5, 229
scale values, manipulating 120
A Scandal in Bohemia (Arthur Conan Doyle)
13±14
Scarpetta, Dr Kay 16±17, 21, 27
scatter diagrams see scatterplots
scatterplots 149±51, 161, 214
Excel 168±71
idiographic 223
Schenkein, Jim 7, 8
Schlegoff, E.A. 5±6
Schuman, Howard 81
Schu
Ètz, Alfred 5
Schwartz, S. 68
scientific writing 234±5
scores, spread 132
Scott, Walter Dill 71
Sebeok, T.A. 37, 231
secondary analysis 25, 30
Sellers, Peter 81
Shakespeare, W. 67±8
Sheffield, F. 73
Sherman, B.L. 24
The Sign of Four (Arthur Conan Doyle) 33,
37, 109
Silver Blaze (Arthur Conan Doyle) 37
Silverman, David 8
Simmat, R. 71, 72
simple linear regression 156±62, 214
simple random sampling 91
Slawski, E.J. 17
Smith, B. 112
Smith, E.R. 89
Smith, H. 161
smoking, and lung cancer 161±2
snowball sampling 95
social data, normal distribution 213±14
Social Distance scale, Bogardus, E.S. 80
social groups, integration 220±2
social norms 58±9
social order, and statistics 213±14
I N D E X
255

Social Research Association 239
social science research
data 30, 213±14
errors 27
public nature 27, 59
quantitative methods 7
reliability of data 6
social surveys 65
Spearman, Charles 215±17
Spencer, Herbert 40
Spillman, D. 24±5
Spock, Dr (Star Trek character) 52
sponsors or funders, relations with/
responsibilities to 243±5
sports psychology 185
spread, scores 132
SPSS
Accounting for Tastes dataset 124±31
boxplots 129
chi-square tests 199
correlation and regression 163±8
data description 138±40
data plotting 122±33
histograms 129
independence testing 208±10
randomization tests 213
two-sample tests 201±4
standard deviation 136±8
standard error 160
standardizing variables 152
statistical analysis, questionnaire results 77
statistical distributions not universal laws
214, 223
statistical information, and case studies 230
The Statistical Inquirer, multimedia
courseware 29, 126
statistical software see Excel; SPSS
statistics
collection 66
and decision-making 39
inferential 93
as a religious service 76
and social order 213±14
see also quantitative techniques
stem and leaf displays 110±13
Stern, P.C. 23
Sternberg, R.J. 119
Stevens, S.S. 45, 63
straight line, equation 158
The Strange Crime of John Boulnois (G.K.
Chesterton) 11±12
stratified random sampling 91, 92
structural equation modelling (SEM) 162
structured interviews 65
A Study in Scarlet (Arthur Conan Doyle) 34,
230
Subjective Computer Experience Scale 112
suicide 218±23
summary statistics 176
summative scales 80±1
surveys 66±7, 75±87
syllogism, valid 38
symmetry, normal distribution 178, 179
systematic sampling 92
t-test 182±3, 186
Excel 211
independent samples 186
related samples 193±5, 211
tabular presentation of data
best practice 118±20
misleading 120±2
Takooshian, H. 75
television viewing, statistical analysis 20,
26±7
testing effects 90
tests, robustness 224
tetrad difference 216±17
The Dutch Shoe Mystery (Raymond
Chandler) 147±8
theoretical sampling 95
theories, testing 27, 29
third person, use in scientific writing 234±5
Thurstone, L.L. 79±80
time, importance in research 25±7, 30
triangulation 95±6, 230
Tukey, J. 110
Tunstall, J. 20
Turner, Roy 7
twin studies 217±18
two-sample tests 185±96, 201±8
two-way tables see contingency tables
U test, Mann±Whitney 189±91, 203
Umiker-Sebeok, J. 37
uncertainty, avoidance 57±9
unimodality of normal distribution 178, 179
unit of analysis 21±2, 24, 30, 51, 92
unordered categories 47±8
US Surgeon General 161
Valentin (French detective) 38
validity
construct 89
external 22, 89, 90±6
internal 89, 90, 96, 103
and reliability 90
I N D E X
256

trade-offs 95
variability 135±8, 143
variable by case matrix 67, 76
variables
categorical 171
confounding and extraneous 75, 162
continuous 47, 48
cultural 55±6
dependent and independent 42, 46
diagramming 42±3
discrete 47, 48
explanatory 156, 160
extraneous 68
not normally distributed 224
operationalization 46, 48
as questionnaire questions 77
response 156, 160
standardizing 152
types 45±8
variance 136±8, 186
voting behaviour 96±102
Wainer, H. 118
Watson, J.B. 71
Watson, R. 47
Weaver, David 18±19
Welch, E.H. 82
Wexford, Inspector 229±30
whiskers (of box plot) 116±17
Whose Body? (Dorothy L. Sayers) 229
Wilcoxon signed rank test 195±6, 207
Wilhoit, Cleveland 18
William of Baskerville 88, 103
Wimsey, Lord Peter 64±5, 229, 232, 235
Windahl, S. 101
within-subjects design 74±5, 193
Wittgenstein, Ludwig 7, 8
wording of questions 83
writing style 234±5
youth crime 2±4
Yule, G.U. 214
z-statistic 190
Z-test 181, 182
Zematis, R. 119
I N D E X
257

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