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i
Analyzing Quantitative Data
From Description to Explanation
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Analyzing Quantitative Data
From Description to Explanation
Norman Blaikie
SAGE Publications
London • Thousand Oaks • New Delhi
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© Norman Blaikie 2003
First published 2003
All rights reserved. No part of this publication may be
reproduced, stored in a retrieval system, transmitted or
utilized in any means, electronic, mechanical, photocopying,
recording or otherwise, without permission in writing from
the Publishers.
SAGE Publications Ltd
6 Bonhill Street
London EC2A 4PU
SAGE Publications Inc.
2455 Teller Road
Thousand Oaks, California 91320
SAGE Publications India Pvt Ltd
32, M-Block Market
Greater Kailash – I
New Delhi 110 048
British Library Cataloguing in Publication data
A catalogue record for this book is available from
the British Library
ISBN 0 7619 6758 3
0 7619 6759 1
Library of Congress Control Number available
Typeset by C&M Digitals (P) Ltd., Chennai, India
Printed in Great Britain The Cromwell Press Ltd, Trowbridge, Wiltshire
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In memory of
my father
George Armstrong Blaikie
whose fascination with numbers was infectious
and
my daughter
Shayne Lishman Blaikie
whose logic was impeccable
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Contents
List of Figures xiv
List of Tables xvi
Acknowledgements xx
Introduction: About the Book 1
1 Social Research and Data Analysis: Demystifying Basic Concepts 10
2 Data Analysis in Context: Working with Two Data Sets 37
3 Descriptive Analysis – Univariate: Looking for Characteristics 47
4 Descriptive Analysis – Bivariate: Looking for Patterns 89
5 Explanatory Analysis: Looking for Influences 116
6 Inferential Analysis: From Sample to Population 159
7 Data Reduction: Preparing to Answer Research Questions 214
8 Real Data Analysis: Answering Research Questions 249
Glossary 306
Appendix A: Symbols 324
Appendix B: Equations 326
Appendix C: SPSS Procedures 333
Appendix D: Statistical Tables 339
References 344
Index 347
Summary Chart of Methods 353
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Detailed Chapter Contents
List of Figures xiv
List of Tables xvi
Acknowledgements xx
Introduction: About the Book 1
Why was it written? 1
Who is it for? 3
What makes it different? 4
What are the controversial issues? 6
What is the best way to read this book? 7
What is needed to cope with it? 8
Notes 9
1 Social Research and Data Analysis: Demystifying Basic Concepts 10
Introduction 10
What is the purpose of social research? 10
The research problem 11
Research objectives 11
Research questions 13
The role of hypotheses 13
What are data? 15
Data and social reality 16
Types of data 17
Forms of data 20
Concepts and variables 22
Levels of measurement 22
Categorical measurement 23
Nominal-level measurement 23
Ordinal-level measurement 23
Metric measurement 24
Interval-level measurement 25
Ratio-level measurement 25
Discrete and continuous measurement 26
Review 26
Transformations between levels of measurement 27
What is data analysis? 28
Types of analysis 29
Univariate descriptive analysis 29
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Bivariate descriptive analysis 29
Explanatory analysis 30
Inferential analysis 32
Logics of enquiry and data analysis 33
Summary 34
Notes 36
2 Data Analysis in Context: Working with Two Data Sets 37
Introduction 37
Two samples 37
Descriptions of the samples 39
Student sample 39
Resident sample 39
Concepts and variables 40
Formal definitions 40
Operational definitions 40
Levels of measurement 43
Data reduction 44
Notes 45
3 Descriptive Analysis – Univariate: Looking for Characteristics 47
Introduction 47
Basic mathematical language 48
Describing distributions 52
Frequency counts and distributions 53
Nominal categories 53
Ordinal categories 54
Discrete and grouped data 55
Proportions and percentages, ratios and rates 59
Proportions 59
Percentages 59
Ratios 61
Rates 62
Pictorial representations 62
Categorical variables 63
Metric variables 64
Shapes of frequency distributions: symmetrical,
skewed and normal 66
Measures of central tendency 68
The three Ms 68
Mode 68
Median 69
Mean 71
Analyzing quantitative data
viii
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Mean of means 74
Comparing the mode, median and mean 75
Comparative analysis using percentages and means 76
Measures of dispersion 77
Categorical data 78
Interquartile range 78
Percentiles 79
Metric data 79
Range 79
Mean absolute deviation 79
Standard deviation 80
Variance 83
Characteristics of the normal curve 84
Summary 87
Notes 87
4 Descriptive Analysis – Bivariate: Looking for Patterns 89
Introduction 89
Association with nominal-level and ordinal-level variables 91
Contingency tables 91
Forms of association 94
Positive and negative 94
Linear and curvilinear 96
Symmetrical and asymmetrical 96
Measures of association for categorical variables 96
Nominal-level variables 97
Contingency coefficient 97
Standardized contingency coefficient 99
Phi 101
Cramér’s V 101
Ordinal-level variables 102
Gamma 102
Kendall’s tau-b 104
Other methods for ranked data 105
Combinations of categorical and metric variables 105
Association with interval-level and ratio-level variables 106
Scatter diagrams 106
Covariance 107
Pearson’s r 108
Comparing the measures 111
Association between categorical and metric variables 113
Code metric variable to ordinal categories 113
Dichotomize the categorical variable 113
Summary 114
Notes 114
Detailed chapter contents
ix
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5 Explanatory Analysis: Looking for Influences 116
Introduction 116
The use of controlled experiments 117
Explanation in cross-sectional research 118
Bivariate analysis 120
Influence between categorical variables 120
Nominal-level variables: lambda 120
Ordinal-level variables: Somer’s d 124
Influence between metric variables: bivariate regression 125
Two methods of regression analysis 128
Coefficients 130
An example 132
Points to watch for 133
Influence between categorical and metric variables 134
Coding to a lower level 134
Means analysis 134
Dummy variables 135
Multivariate analysis 136
Trivariate analysis 136
Forms of relationships 136
Interacting variables 137
The logic of trivariate analysis 138
Influence between categorical variables 141
Three-way contingency tables 141
An example 141
Other methods 145
Influence between metric variables 146
Partial correlation 146
Multiple regression 146
An example 148
Collinearity 150
Multiple-category dummy variables 150
Other methods 153
Dependence techniques 153
Analysis of variance 154
Multiple analysis of variance 154
Logistic regression 154
Logit logistic regression 154
Multiple discriminant analysis 154
Structural equation modelling 154
Interdependence techniques 155
Factor analysis 155
Cluster analysis 155
Multidimensional scaling 155
Summary 156
Notes 158
x
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6 Inferential Analysis: From Sample to Population 159
Introduction 159
Sampling 160
Populations and samples 160
Probability samples 161
Probability theory 163
Sample size 166
Response rate 167
Sampling methods 168
Parametric and non-parametric tests 171
Inference in univariate descriptive analysis 172
Metric variables 175
Inference in bivariate descriptive analysis 177
Testing statistical hypotheses 178
Null and alternative hypotheses 179
Type I and type II errors 180
One-tailed and two-tailed tests 181
The process of testing statistical hypotheses 182
Testing hypotheses under different conditions 183
Some critical issues 185
Nominal-level data 189
Ordinal-level data 191
Comparing means 192
Group t test 193
Mann–Whitney U test 197
Analysis of variance 201
Test of significance for Pearson’s r 204
Inference in explanatory analysis 205
Nominal-level data 205
Ordinal-level data 206
Bivariate regression 208
Summary 209
Notes 212
7 Data Reduction: Preparing to Answer Research Questions 214
Introduction 214
Scales and indexes 214
Creating scales 215
Environmental Worldview scales and subscales 215
Pre-testing the items 216
Item-to-item correlations 217
xi
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Item-to-total correlations 217
Cronbach’s alpha 219
Factor analysis 220
Willingness to Act scale 238
Indexes 239
Avoidance of environmentally damaging products 240
Support for environmental groups 240
Recycling behaviour 240
Recoding to different levels of measurement 241
Environmental Worldview scales and subscales 242
Recycling index 243
Age 243
Characteristics of the samples 244
Summary 246
Notes 248
8 Real Data Analysis: Answering Research Questions 249
Introduction 249
Environmental Worldview 250
Environmentally Responsible Behaviour 252
Bivariate descriptive analysis 257
Environmental Worldview and Environmentally
Responsible Behaviour 258
Comparing metric and categorical variables 262
Conclusion 263
Age, Environmental Worldview and Environmentally Responsible
Behaviour 264
Gender, Environmental Worldview and
Environmentally Responsible Behaviour 268
Explanatory analysis 270
Bivariate analysis 273
Categorical and metric variables: means analysis 276
Multivariate analysis 277
EWVGSC and WILLACT with ERB 279
WILLACT, Age and Gender with ERB 282
Categorical and metric variables: means analysis 285
EWVGSC and WILLACT with ERB 286
WILLACT and Gender with ERB 287
xii
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Partial correlation 292
Conclusion 303
Notes 304
Glossary 306
Appendix A: Symbols 324
Appendix B: Equations 326
Appendix C: SPSS Procedures 333
Appendix D: Statistical Tables 339
References 344
Index 347
Summary Chart of Methods 353
xiii
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List of Figures
3.1 Religion (Students): bar chart 63
3.2 Religion (both samples): bar chart 64
3.3 Religiosity (both samples): bar chart 64
3.4 Religion (Students): pie chart 65
3.5 Religiosity (Students): pie chart 65
3.6 Age (both samples): line graphs 66
3.7 Examples of symmetrical distributions 67
3.8 Median to one decimal place 71
3.9 Environmental Worldview (both samples): line graphs 77
3.10 Environmental Worldview (combined samples): line graph 77
3.11 Area covered under the normal curve by
one to three standard deviations 86
4.1 Parts of a table 92
4.2 Scatter diagram: Environmental Worldview by Age (Residents) 107
4.3 Scatter diagram: Environmental Worldview
by Age (subsample of Residents) 109
5.1 Scatter plot of weekly hours worked by weekly wages 127
5.2 Residuals from a regression line (hypothetical data) 131
5.3 Possible forms of relationships between three variables 137
6.1 Distributions of mean ages of 20 samples 164
6.2 Types and methods of sampling 170
6.3 Confidence intervals for mean Age by
sample size (Resident sample) 177
7.1 Scree plot of eigenvalues for 24 items (combined samples) 223
7.2 Scree plot of eigenvalues for 14 items (combined samples) 227
7.3 Scree plot of eigenvalues for nine items (combined samples) 229
7.4 EWVGSC mean scores (combined samples) 233
7.5 HUSENV mean scores (combined samples) 233
7.6 GOVCONT mean scores (combined samples) 233
7.7 ECGROW mean scores (combined samples) 234
7.8 SCITEK mean scores (combined samples) 234
7.9 IMPACT mean scores (combined samples) 234
7.10 ALTENGY mean scores (combined samples) 235
7.11 WILLACT mean scores (combined samples) 239
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List of figures
xv
8.1 EWVGSC categories (both samples) 253
8.2 WILLACT categories (both samples) 255
8.3 Support Groups (both samples) 256
8.4 Avoid Products (both samples) 256
8.5 Recycling index (both samples) 257
8.6 Support Groups by WILLACT controlled for
Gender (Students) 288
8.7 Avoid Products by WILLACT controlled for
Gender (Students) 289
8.8 Support Groups by WILLACT controlled for
Gender (Residents) 290
8.9 Avoid Products by WILLACT controlled
for Gender (Residents) 290
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List of Tables
1.1 Research questions and objectives 14
1.2 Levels of measurement 27
3.1 Raw data on Religion (Students) 53
3.2 Distribution by Religion (both samples) 53
3.3 Distribution by Religiosity (both samples) 54
3.4 Age distribution in years (Students) 55
3.5 Age distribution in five categories (Students) 56
3.6 Age distribution in six categories (Residents) 56
3.7 Number of children (Residents) 57
3.8 Number of children (subsample of Residents) 57
3.9 Comparison of Student and Resident samples by Age 58
3.10 Comparison of Gender proportions (both samples) 60
3.11 Age in years (Residents) 70
3.12 Calculation of mean Age in years (Residents) 73
3.13 Mean of Age distributed in ten categories (Residents) 73
3.14 Mean of two means (both samples) 74
3.15 Mean of two Age category percentages (both samples) 75
3.16 Deviations from the mean of Age in years (Residents) 81–82
4.1 Religion by Gender (Residents; observed and
expected frequencies, and percentages) 92
4.2 Environmental Worldview by Age (Residents;
observed frequencies and percentages) 94
4.3 Environmental Worldview by Age (percentages) 95
4.4 Religion by Gender (Residents; observed frequencies) 99
4.5 Calculation of gamma (from Table 4.2) 103
4.6 Mean deviation method for computing r
(subsample of Residents) 110
4.7 Raw score method for computing r
(subsample of Residents) 110
4.8 Education by Age (percentages; Residents) 113
5.1 Occupation by Religion (Residents; observed
frequencies and percentages) 122
5.2 Occupation by Religion (subsample of Residents) 123
5.3 Occupation by Religion (subsample of Residents; 2 by 2 table) 124
5.4 Working hours per week and weekly wage 126
5.5 Unexplained variation and standard error of the
estimate (subsample of Residents) 132
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List of tables
xvii
5.6 A means analysis of Education and Environmental
Worldview (Residents) 135
5.7 Forms of relationships between three variables 139
5.8 Environmental Worldview and Age (Residents) 142
5.9 Environmental Worldview and Age controlled
for Education (Residents) 143
5.10 Environmental Worldview and Age controlled for
5.11 Regression of Environmental Worldview on Age,
Gender and Education (Residents) 148
5.12 Regression of Environmental Worldview on Age,
Gender and Education in five categories (Residents) 151
5.13 Correlation matrix for Age, Gender and
six Education dummy variables (Residents) 152
5.14 Regression of Environmental Worldview on
Age, Gender and Education, Marital Status,
Religion and Political Party Preference (Residents) 152
6.1 Hypothetical sampling 163
6.2 Variations in confidence intervals of mean Age
by confidence level and sample size (Residents) 176
6.3 Type I and type II errors 181
6.4 Ranked Environmental Worldview scores by
Gender (subsample of Students) 200
6.5 Cells and their ‘diagonals’ in Table 4.2 208
7.1 Correlation matrix of 24 items (both samples) 218
7.2 Unidimensionality, reliability and commonalities
of 24 items (combined samples) 219
7.3 Commonalities and unrotated factors with
24 items (combined samples) 222
7.4 Rotated solution for five factors with 24 items
(combined samples) 225
7.5 Rotated solution for six factors with 24 items
(combined samples) 226
7.6 Unrotated and rotated solutions with 14 retained
items (combined samples) 228
7.7 Unidimensionality and reliability of 10 rejected
7.8 Unrotated and rotated solutions with nine rejected
7.9 Distributions on the 24 items (combined samples) 231
7.10 Distributions on scales and subscales (combined samples) 232
7.11 Reliability of scales and subscales (combined samples) 236
7.12 Correlation matrix of EWV scales and
subscales (combined samples) 237
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xviii
7.13 Unrotated and rotated solutions with Willingness
to Act items (combined samples) 238
7.14 Reliability of behavioural scales (combined samples) 239
7.15 Characteristics of both samples 245
8.1 Sample comparisons of Environmental
Worldview metric variables 250
8.2 Sample comparisons of Environmental
Worldview categorical variables (percentages) 252
8.3 Sample comparison of Environmentally
Responsible Behaviour metric variables 253
8.4 Sample comparison of Environmentally Responsible
Behaviour categorical variables (percentages) 254
8.5 Correlation matrix for EWV and ERB variables
(Pearson’s r; Students) 258
8.6 Correlation matrix for EWV and ERB
variables (Pearson’s r; Residents) 259
8.7 Cross-tabulations between EWVGSC and WILLACT,
Support Groups, Avoid Products and Recycling
(percentages; both samples) 260
8.8 Correlation matrix for EWV and
ERB variables (gamma; Students) 261
8.9 Correlation matrix for EWV and
ERB variables (gamma; Residents) 262
8.10 Cross-tabulations of Support Groups with
WILLACT (percentages; both samples) 263
8.11 EWV and ERB by Age (Pearson’s r and gamma; Residents) 265
8.12 EWV and ERB means and standard deviations by Age (Residents) 265
8.13 Cross-tabulation for Age with EWVGSC, IMPACT, WILLACT,
Recycling, Support Groups and Avoid Products
(percentages; Residents) 267
8.14 EWV and ERB by Gender (Pearson’s r and G; both samples) 268
8.15 EWV and ERB means and standard deviations by
Gender (both samples) 269
8.16 Cross-tabulation of Gender with EWVGSC, SCITEK, WILLACT,
Recycling, Support Groups and Avoid Products
8.17 Influence of EWVGSC and WILLACT on
Support Groups and Avoid Products
8.18 Means analysis of Gender and Religion
(Students), and Age, Gender and Religion
(Residents), with Support Groups and Avoid Products 276
8.19 Regression of ERB variables on WILLACT and
EWVGSC (both samples) 277
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List of tables
xix
8.20 Influence of EWVGSC on Support Groups and
Avoid Products controlled for WILLACT
(percentages; Students) 280
8.21 Influence of WILLACT on Support Groups
and Avoid Products controlled for
EWVGSC (percentages; Students) 281
8.22 Influence of EWVGSC and WILLACT on Support
Groups and Avoid Products with controls for
WILLACT and EWVGSC (Residents) 282
and Avoid Products controlled for Gender
and Avoid Products controlled for Age (Residents) 284
8.25 Means analysis of EWVGSC on Support Groups
and Avoid Products controlled for WILLACT (Students) 285
8.26 Means analysis of WILLACT on Support
Groups and Avoid Products controlled for
EWVGSC (Students) 287
Groups and Avoid Products controlled
for Gender (Students) 288
Groups and Avoid Products controlled for
Groups and Avoid Products controlled for Age (Residents) 291
8.30 WILLACT by Support Groups and Avoid Products
controlled for EWVGSC (Pearson’s r; both samples) 293
8.31 Regression of ERB variables on EWVGSC,
WILLACT and Gender (Students) 295
8.32 Regression of ERB variables on EWVGSC,
WILLACT, Age and Gender (Residents) 296
8.33 Correlation matrix of potential predictor
variables (Pearson’s r; Residents) 298
8.34 Regression of Support Groups on selected
predictor variables (Residents) 300
8.35 Regression of Avoid Products on selected
predictor variables (Residents) 302
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Acknowledgements
I am indebted to my early mentors in data analysis, in particular, Charles Gray
and Oscar Roberts, for providing this novice researcher with necessary knowledge
about which textbooks were usually silent. I am also appreciative of the numer-
ous students who, over many years, have stimulated me to think through the
relationship between social science statistics and social research practice.
The data set derived from the sample of residents in the former City of
Box Hill, Melbourne, and which has been used to illustrate the data analysis
procedures, was produced with the assistance of Malcolm Drysdale, students
from the Socio-Environmental Assessment and Policy degree at the RMIT
University, and the university’s research funding sources. My thanks also go to
my wife Catherine for invaluable assistance with the data entry of both of this
and the Student sample data set.
Without Chris Rojek’s invitation and challenge to write this book, I would
never have contemplated committing three years of my life to such a task. I am
grateful to Chris, and Kay Bridger at Sage, for their support through the
demanding process of its accomplishment. I am particularly indebted to Richard
Leigh for not only forcing me to think through some tricky technical issues at
the copy-editing stage, but also for computing the statistical tables in Appendix
D. The latter enabled me to have accurate tables, in the format that I wanted,
and not to have to rely on less suitable existing tables.
Norman Blaikie
xx
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Introduction: About the Book
This book is about how to use quantitative data to answer research questions in
social research. It is about how to analyze data in the form of a set of variables
that have been measured on a collection of individuals or that have been
collected about some aspects of social life. This is not a book on statistics,
although it covers an array of statistical procedures. It is not a book on research
methods, although it deals with some of the methods essential for quantitative
social research. It is not a book on how to use statistical software packages,
although it refers to such procedures.
Why was it Written?
This is not a book I ever imagined writing. My first reaction when asked
to write it was: ‘Why do we need another book on statistics or data analysis?
Hasn’t it all been said already?’ Perhaps the reason why so many books continue
to be written in this field is that their authors think they can make an improve-
ment to the way students are introduced to a course that most find excruciat-
ingly difficult. This is a worthy aim and was part of my brief. However, the
challenge that I was given, and which got me hooked, was to be iconoclastic. I
interpreted this to include: challenging unhelpful content and structure that
have been taken for granted in successive volumes in the field; being critical of
practices that have been perpetuated without having any obvious use to a
researcher; and, more particularly, exposing the misuses of certain procedures.
Given that I have spent much of my academic career doing just these things in
some other areas of my discipline, I could not resist taking up the challenge of
putting in writing concerns that I have had about some of the practices in this
area of social research.
Like Merton (1968) and Mills (1959), I have been very critical of some forms
of mindless empiricism as well as the use of highly sophisticated research tech-
niques that create great gulfs between the researcher and the social reality that
is being studied (see, for example, Blaikie, 1977, 1978, 1981). However, in
spite of this, I believe that quantitative data analysis is important for certain
purposes. But it is not the only form of analysis. There are areas of social
research where qualitative methods of data collection and analysis are much
more appropriate, if not absolutely essential. The trick is to know which methods
to use in which context and for which purpose.
Initially, I set out to cover both quantitative and qualitative data analysis.
However, this turned out to be an unmanageable task and a decision was made
to concentrate on only quantitative data analysis at this stage.
3055-Introduction.qxd 1/10/03 10:32 AM Page 1

The key question behind the structure and content of the book has been
what students and novice researchers in the social sciences need to know in
order to be able to analyze data from group or individual research projects in
which they are likely to be involved. In considering what to cover and how to
organize it, I decided to abandon tradition in favour of addressing this pragmatic
issue. This decision was largely influenced by my experience in teaching a tradi-
tional undergraduate course in statistics to students in a degree programme that
essentially trained applied social researchers. I kept asking myself what
relevance much of the course was likely to have for these students in both
the short term and the longer term. What was clearly missing, and had to be
covered in other contexts, was practical knowledge about how to actually analyze
the results obtained in real research projects.
There was another reason. I had had many unhelpful experiences doing
statistics courses when a student. In looking for guidance on how to analyze
data, I also found books on statistics extremely unhelpful; books on data analysis
were unheard of then. Statistics books seemed to be concerned with issues and
procedures that had little to do with the kind of research I was doing. In
the end, I had to rely on advice from a few seasoned researchers who had dis-
covered, mainly by trial and error, what was required. So this is the book that
I wish had been available when I was a student and novice researcher.
In spite of being competent in basic mathematics, and having earlier earned
a living for twelve years in a profession that is based on the use of applied mathe-
matics, I found courses and textbooks on statistics unnecessarily difficult to
follow. They used an alienating language, included confusing symbols and covered
topics that were largely irrelevant to my needs. I kept asking myself: ‘Why am
I doing this?’
Courses in statistics are a common requirement in most social science disci-
plines. Some academics seem to operate on the idea that going through the
trauma of doing such a course is a necessary right of passage for each generation
of social scientists. If you cannot cope with statistics you are not permitted to
call yourself a genuine social scientist. No doubt, an earlier justification for such
courses would have been to give social scientific discipline scientific status. This
is still true in psychology.
Rather than producing highly trained statisticians, these courses are more
likely to produce traumatized and demoralized students. They may also keep
potential majors in the disciplines away. Let’s face it, programmes in the social
sciences usually attract students with limited mathematical ability who are
often refugees from high school maths classes. The social sciences are chosen
because they are thought to provide a safe haven from the trauma of numbers
and symbols. Then a course in statistics appears on the horizon to rekindle the
old anxieties. What these students need is to be given confidence that they can
do basic analysis, and that they can understand what is required and why. In any
case, most of what is learned in these courses is quickly forgotten unless it has
direct relevance to real research activities.
There is no point in expecting undergraduates to master what is normally
covered in statistics texts if they are unlikely to ever use it. While it might
be nice to know the theory behind statistical procedures, such as probability
2

theory and the method of least squares, as well as the intricate details of many
complex equations, what most students need is to know what methods to use
for analyzing certain kinds of data, and why. Most of their requirements
are pretty basic, or can be kept basic by addressing research questions in a
manageable way.
In my experience, teachers of courses in statistics fall into two main cate-
gories. There are those who treat mathematically challenged students as
imbeciles and delight in inflicting great stress and discomfort on them. I have
encountered a few of these. On the other hand, there are those who try very
hard to make statistics intelligible to students whose mathematical abilities are
minimal or who have already convinced themselves that it is just too difficult
for them.
I suspect some of my readers will suffer from the common malady of ‘symbol
phobia’. Presented with a simple equation, such as a + b = c, your eyes will
glaze over. Or perhaps, like the well-known Indian writer, R.K. Narayan, you
suffer from what he called ‘figure-blindness’. In his essay on ‘Higher mathe-
matics’, he argued that it is inappropriate to describe arithmetic as elementary
mathematics. In his experience, arithmetic has more terrors than algebra and
geometry:
My mind refuses to work when it encounters numbers. Everything that has anything
to do with figures is higher mathematics to me. There is only one sort of mathe-
matics in my view and that is the higher one. To mislead young minds by classify-
ing arithmetic as elementary mathematics has always seemed to me as a base trick.
A thing does not become elementary by being called so. … However elementary we
may pretend arithmetic to be, it ever remains puzzling, fatiguing and incalculable.
(Narayan, 1988: 11)
Well, this book contains symbols, but only very basic ones, and requires com-
petence in basic arithmetic. However, many of the conventions used in statis-
tics texts are avoided, often by expressing symbols in words. This strategy may
upset some of the purists – although even they do not always agree on which
symbols to use – but I am prepared to risk this in order to take some of the
mystique out of reasonably simple ideas.
Who is it for?
Analyzing Quantitative Data is intended for students in the social sciences.
It is designed to meet the needs of average undergraduate and most post-
graduate students, and to do this in a way that relates directly to the business
of doing social research. The book can be used in courses on quantitative data
analysis where such courses complement others on data-gathering techniques.
It could be used in a broad-ranging course on research methods when this
encompasses methods of both data gathering and data analysis. Where degree
programmes have a research practicum, with either individual or group
Introduction
3

projects, this book should be a useful companion for students doing
quantitative research.
The book will also be a useful reference for postgraduate students who are
required to undertake a major or minor quantitative research project. For many
students, this is the first opportunity to undertake their own research. It usually
involves designing a project from scratch (see Blaikie, 2000), collecting data,
analyzing it and then writing a thesis or major report. Among many other things,
the design stage requires decisions to be made about the methods of data analy-
sis to be used, and then later the analysis will need to be undertaken. When
quantitative analysis is involved, based on a set of variables and a substantial
sample, this book should help smooth the way.
While I have written the book with sociologists in mind, it will be useful for
a range of social science and related disciplines. In fact, it will be useful for any-
one who is required to undertake social research. This includes researchers
from fields such as political science, social psychology, human geography, urban
studies, education, nursing, business studies, management, mass communica-
tions, environmental studies and social work. It may also be useful for some
kinds of research in economics and other areas of psychology.
Analyzing Quantitative Data will also be useful for novice social researchers
anywhere. Academics outside the social sciences, as well as employees in the
public and private sectors, may be called on to undertake social research of some
kind. Alternatively, they may not be required to actually do any research but may
need to commission someone else to do it, to oversee such research, or to evalu-
ate research produced by social scientists. The book will be a useful reference.
What Makes it Different?
There are a number of features of the book that make it different from most if
not all books presently available in this field. First, two classification schemes
are used to organize the discussion of the many methods of data analysis. One
is the type of analysis, and the other is the level of measurement. Types of analy-
sis are classified as univariate description, bivariate description (association),
explanation and inference. The levels of measurement are divided into two
broad categories, categorical and metric, the former subdivided into nominal
and ordinal levels, the latter into interval and ratio levels. These categories will
be explained in due course. Each of the four key chapters (3–6) deals with one
type of analysis, and each chapter is subdivided into sections that deal with the
different levels of measurement. The reason for this is that different methods
of analysis are appropriate for each type of analysis as well as for the different
levels of measurement within each type. Keeping these distinctions clear should
make the purpose of the wide array of procedures easier to understand and to
select. Surprisingly, this scheme appears to be rather novel.1
Second, all the methods of analysis are illustrated and discussed in the
context of a real research problem. In many ways, the whole book simulates the
4

kind of considerations and processes social researchers are likely to have to go
through in analyzing their data. This approach to statistics, let alone data analysis,
is extremely rare.2
Two data sets from a research programme are used through-
out the book. The data sets are typical of those obtained from small to moderate-
sized social surveys. Both are from my research programme on environmentalism
and cover the same variables. While the research topic is specific, the methods of
analysis are universal. They can certainly be generalized to almost any study on
the relationship between attitudes (or worldviews) and behaviour.
The data sets will be explained in Chapter 2, analyses of certain variables will
be used as examples in Chapters 3–7, and in Chapter 8 a set of research ques-
tions are answered using these data with the appropriate procedures. The book
takes the reader through a wide range of methods of analysis, illustrates their
application with the two data sets, and concludes by putting the methods into
practice in a ‘real’ research project.
Third, the nature of data, particularly quantitative data, is discussed rather
than being taken for granted. What is accepted as being appropriate and reliable
data is dependent on the ontological and epistemological assumptions that are
adopted. These issues are clearly ignored in most if not all textbooks on research
methods, data analysis and statistics. This will be addressed in Chapter 1.
Fourth, in addition to being concerned with the nature of data and the appro-
priate procedures for analyzing them, the use of the two data sets provides an
excellent opportunity to combine data analysis with the interpretation of the
products. In fact, in the process of answering the set of research questions in
Chapter 8, it is also necessary to interpret the results. Therefore, not only will
the illustrations be set in the context of real research, but also the results will
have to be interpreted within this context. This extremely important aspect of
data analysis is generally missing in most textbooks because the illustrations do
not have a consistent context from which they are drawn.
Fifth, this is a software-free textbook. There is a growing trend in textbooks
on statistics and data analysis to include instruction on how to do the various
methods of analysis using one of the popular statistical software packages, such
as SPSS or Minitab. If you require such a book you could consult examples such
as Bryman and Cramer (1997), Fielding and Gilbert (2000), Field (2000) and
Foster (2001). I have decided not to follow this trend for a number of reasons.
First, while a software package such as SPSS is very popular, it is possible that
you may be required to or choose to use some other software. Second, software
packages are updated regularly, and this can include changes to the screen layouts.
A textbook based on a particular version will soon become out of date, or would
need to be revised frequently. Third, there is a common temptation to go
straight to the software package without first understanding the various proce-
dures and why they are used. Hence, this book focuses on the principles behind
the procedures, on the procedures themselves, and on the purposes for which
they should be used. It is not difficult to learn how to use a software package;
I have found a three-hour workshop sufficient to introduce students to the
setting up of a database, to entering data and to doing basic analysis. It should
not be difficult to relate what is learnt in such a course, or from a suitable book,
to what is covered in this book. Frankly, if you know what it is that you need to
Introduction
5

be doing, most statistical software packages are now sufficiently user-friendly
for any moderately competent user to find their way about without much
difficulty. In SPSS, for example, it is just a matter of finding the appropriate
pull-down menu and then the method of analysis that you need. Selecting the
appropriate statistics is an easy matter – that is, if you know what you should
be doing. However, I have made one gesture in the direction of software.
Appendix C sets out the basic steps that are used in recent versions of SPSS to
carry out most of the procedures covered in the book.
The sixth difference is not as critical as the previous ones. It refers to the fact
that the book is about methods of data analysis, not statistics as such. It is
intended for practitioners, not just to satisfy course requirements. It is designed
to complement courses and textbooks that concentrate on methods of data
collection by providing a wide review of how quantitative data can be handled
in the pursuit of answers to research questions. However, it does not shy away
from a consideration of the equations that are used in the more basic procedures.
What are the Controversial Issues?
The following icons of social research are challenged and are either modified or
destroyed in the following chapters:3
1. That social research must begin with one or more hypotheses.
2. That tests of significance are an essential feature of data analysis.
3. That measures of association provide explanations.
The following case will be made about the first issue:
• All social research must start out with one or more research questions.
• There are three types of research questions: ‘what’ questions seek descrip-
tions; ‘why’ questions seek explanations; and, ‘how’ questions seek inter-
vention for change.
• Only ‘why’ questions that are being answered with the aid of theory require
the use of hypotheses.
• In any case, there are two types of hypotheses: theoretical hypotheses are
derived from theory to provide tentative answers to ‘why’ questions; statis-
tical hypotheses are used in the process of generalizing data from a random
sample to the population from which the sample was drawn.
• A great deal of confusion is created by a general lack of recognition of the
differences between these two types of hypotheses.
• Theoretical hypotheses are only relevant when certain types of ‘why’ ques-
tions need to be answered, and statistical hypotheses are only relevant when
data come from a random sample. While some research may require both
types of hypotheses, other research may require only one type, and a great
deal of research requires neither type. However, all research requires research
questions.
6

• Some research, of the theory-generating variety, ends up with hypotheses or
theory rather than staring out with them.
Tests of significance are probably the most misunderstood and misused
aspect of data analysis. The following argument is made about their use:
• Tests of significance can provide no help to a researcher in making decisions
about the importance or meaning of research results.
• They are not measures of association.
• They are only appropriate when statistical hypotheses are being tested, that
is, when population parameters are being inferred from sample statistics.
• They can only be used with sample data that are derived from a population
using probability procedures.
• They are inappropriate when samples are drawn using non-probability pro-
cedures or when data come from a population; performing this statistical
ritual in these circumstances has absolutely no meaning.
• They cannot be used to test theoretical hypotheses, although, in some cir-
cumstances, they may be used as a stepping-stone on the way to such test-
ing, that is, when probability samples are being used.
• They are no help in generalizing beyond the population selected for study;
further generalization is a matter of judgement based on other kinds of evidence.
The third issue is now well recognized but still causes confusion. It is
concerned with the purpose of establishing correlations between variables:
• Descriptive research consists of establishing characteristics of particular
phenomena, trends in these characteristics over time and patterns in the
connections between phenomena.
• Measures of association establish the strength of patterns or connections
between variables; they are an elaborate form of description.
• While such description may provide some understanding of phenomena and,
some would argue, provide a basis for making predictions, they cannot
answer ‘why’ questions.
• However, such patterns have to be established before explanation can be
undertaken.
• Explanation tells us why patterns or trends exist.
These arguments indicate the position I have taken on some of the common
misunderstandings in data analysis.
What is the Best Way to Read this Book?
The answer is simple: start at the beginning and work through to the end. The
topics covered chapter by chapter build on each other. There is a developmental
Introduction
7

progression from the most elementary forms of analysis to the more complex.
In addition, themes and arguments also run through the chapters. Without
an overview of these, it will be very easy to take any method of analysis out of
context.
I am aware that many students approach books just to find a specific concept
or topic. Once the knowledge and skills dealt with in this book have been
mastered, this ‘dipping in’ approach will no doubt be appropriate when it is
necessary to be refreshed about specific types of analysis. If this is the only way
the book is used, it will still be useful. However, an understanding of the ‘bigger
picture’ is necessary to avoid making incorrect selections or interpretations of
methods of data analysis.
What is Needed to Cope with it?
To understand data analysis successfully, it is very useful to have or to be able
to develop a fascination with numbers, to:
• enjoy manipulating them to find answers;
• be able to understand what they are telling you; and
• have a sense of when they appear to be correct or not.
Of course, you need to have some basic numerical skills, to be able to add, sub-
tract, multiply and divide, and you need to be able to understand the conven-
tions used in mathematical equations, to know how to enter data into them and
how to manipulate them. A short refresher course on these skills is included in
the first part of Chapter 3.
To undertake data analysis in a mechanical and cookbook fashion can be not
only unsatisfying but also dangerous. It is important to be able to understand
when certain procedures should be used and what they are designed to achieve.
It is also helpful to be able to understand what principles are involved and why
certain requirements must be satisfied. I cannot guarantee that after reading
through and working with this book you will feel completely confident about
these things. This will only come with practical experience.
Lastly, I am not a statistician, although I have great admiration for such
experts. I am a sociologist who, among other things, does social research and
teaches courses on epistemology and a wide range of social research methods.
As a teacher, I am constantly challenged with the task of helping students, par-
ticularly postgraduate students, to think like researchers, to develop a research
imagination. This requires being able to conceptualize a problem and to design
a research project that will address it. This challenge has led to two earlier
books, one on the philosophy of social research, in particular on the strategies
or logics of enquiry that can be used in the social sciences (Blaikie, 1993a), and
the other on the many decisions that need to be considered in designing such a
project (Blaikie, 2000). Analyzing Quantitative Data is a logical extension of
8

these two. My task is to try to take the mystery and anxiety out of the analysis
stage of social research without trivializing it in the process; to be simple but
not simplistic. I shall have to leave the reader to be the judge of whether I have
been successful.
Notes
1
Cramer (1994) goes some way in this direction by identifying levels of measurement clearly
but types of analysis less clearly.
2
Some attempts have been made to use data from a particular source to illustrate the pro-
cedures. For example, Babbie et al. (2000) use data from the United States General Social
Survey to explore issues. Bryman and Cramer (1997) use two projects to illustrate some proce-
dures, and de Vaus (1995) goes partly in this direction with a chapter in which data from one
of the author’s own studies are used to provide an overview of the methods that have been dis-
cussed. While these are all helpful approaches to data analysis, the first example uses a data set
that most individual researchers are unlikely to produce themselves, and the other two exam-
ples do not explore a data set consistently throughout the book.
3
In order to discuss these, it is necessary to use some technical concepts that will not be
elaborated until later chapters. Therefore, the discussion in this section is intended for readers
who have at least some basic familiarity with the concepts of statistics.
Introduction
9

1
Social Research and Data Analysis:
Demystifying Basic Concepts
Introduction
This book is about the analysis of certain kinds of data, that is, only quantitative
data. We need to begin by discussing the three concepts that make up the main
title of this book. The core concept is ‘data’. On the surface, it appears to be a
simple and unproblematic idea. However, lurking behind it are complex and
controversial philosophical and methodological issues that need to be considered.
This concept is qualified by the adjective ‘quantitative’, thus indicating that only
one of the two main types of data in the social sciences will be discussed. Just
what constitutes ‘quantitative’ data will be clarified. The purpose of the book
is to discuss methods of ‘analysis’ used in the social sciences, methods by which
research questions can be answered. The variety of methods that are available
for basic analysis will be reviewed.
This chapter deals with three fundamental questions:
• What is the purpose of social research?
• What are data?
• What is data analysis?
The chapter begins with a discussion of the role of research objectives, research
questions and hypotheses in achieving the purpose of research. This is followed
by a consideration of the relationship between social reality and the data we
collect, and of the types and forms of these data. Included is a discussion of
‘concepts’ and ‘variables’, the ways in which concepts can be measured, and the
four levels of measurement. The chapter concludes with a review of the four
main types of data analysis that are covered in subsequent chapters.1
Let us
start with the first question.
What is the Purpose of Social Research?
The aim of all scientific disciplines is to advance knowledge in their field, to
provide new or better understanding of certain phenomena, to solve intellectual
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puzzles and/or to solve practical problems. Therefore, the critical issues for any
discipline are the following:
• What constitutes scientific knowledge?
• How does scientific knowledge differ from other forms of knowledge?
• How do we judge the status of this knowledge? With what criteria?
• How do we produce new knowledge or improve existing knowledge?
In order to solve both intellectual and practical puzzles, researchers have to
answer questions about what is going on, why it is happening and, perhaps, how
it could be different. Therefore, to solve puzzles it is necessary to pose and
answer questions.
The Research Problem
A social research project needs to address a research problem. In order to do
this, research questions have to be stated and research objectives defined;
together they turn a research problem into something that can be investigated.
Throughout this book the following research problem will be addressed: the
apparent lack of concern about environmental issues among many people and
the unwillingness of many to act responsibly with regard to these issues. This is a
very broad problem. In order to make it researchable, it is necessary to formu-
late a few research questions that can be investigated. These questions will be
elaborated in Chapter 2. In the meantime, to illustrate the present discussion,
let us examine two of them here:
• To what extent is environmentally responsible behaviour practised?
• Why are there variations in the levels of environmentally responsible
behaviour?
Each research question entails the pursuit of a particular research objective.
Research Objectives
One way to approach a research problem is through a set of research objectives.
Social research can pursue many objectives. It can explore, describe, under-
stand, explain, predict, change, evaluate or assess aspects of social phenomena.
• To explore is to attempt to develop an initial rough description or, possibly,
an understanding of some social phenomenon.
• To describe is to provide a detailed account or the precise measurement and
reporting of the characteristics of some population, group or phenomenon,
including establishing regularities.
Social research and data analysis
11
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• To explain is to establish the elements, factors or mechanisms that are
responsible for producing the state of or regularities in a social phenomenon.
• To understand is to establish reasons for particular social action, the occur-
rence of an event or the course of a social episode, these reasons being
derived from the ones given by social actors.
• To predict is to use some established understanding or explanation of a pheno-
menon to postulate certain outcomes under particular conditions.
• To change is to intervene in a social situation by manipulating some aspects
of it, or by assisting the participants to do so, preferably on the basis of
established understanding or explanation.
• To evaluate is to monitor social intervention programmes to assess whether
they have achieved their desired outcomes, and to assist with problem
solving and policy-making.
• To assess social impacts is to identify the likely social and cultural conse-
quences of planned projects, technological change or policy actions on social
structures, social processes and/or people.
The first five objectives are characteristic of basic research, while the last
three are likely to be associated with applied research. Both types of social
research deal with problems: basic research with theoretical problems, and
applied research with social or practical problems. Basic research is concerned
with advancing fundamental knowledge about the social world, in particular
with description and the development and testing of theories. Applied
research is concerned with practical outcomes, with trying to solve some
practical problem, with helping practitioners accomplish tasks, and with the
development and implementation of policy. Frequently, the results of applied
research are required immediately, while basic research usually has a longer
time frame.
A research project may pursue just one of these objectives or perhaps a com-
bination of them. In the latter case, the objectives are likely to follow a
sequence. For example, the four research objectives of exploration, description,
explanation and prediction can occur as a sequence in terms of both the stages
and the increasing complexity of research. Exploration may be necessary to pro-
vide clues about the patterns that need to be described in a particular phe-
nomenon. Exploration usually precedes description, and description is necessary
before explanation or prediction can be attempted. Whether all four objectives
are pursued in a particular research project will depend on the nature of the
research problem, the circumstances and the state of knowledge in the field.
The core of all social research is the sequence that begins with the descrip-
tion of characteristics and patterns in social phenomena and is followed by an
explanation of why they occur. Descriptions of what is happening lead to ques-
tions or puzzles about why it is happening, and this calls for an explanation or
some kind of understanding. The two research questions stated in the previous
subsection illustrate these two research objectives. To be able to explain why
people differ in their level of environmentally responsible behaviour, we need
to first describe the range in levels of this behaviour. The first question is
concerned with description and the second with explanation.
12
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Research Questions
To pursue such objectives, social researchers need to pose research questions.
Research questions define the nature and scope of a research project. They:
• focus the researcher’s attention on certain puzzles or issues;
• influence the scope and depth of the research;
• point towards certain research strategies and methods of data collection and
analysis;
• set expectations for outcomes.
Research questions are of three main types: ‘what’ questions, ‘why’ questions
and ‘how’ questions:
• ‘What’ questions seek descriptive answers.
• ‘Why’ questions seek understanding or explanation.
• ‘How’ questions seek appropriate interventions to bring about change.
All research questions can and perhaps should be stated as one of these three
types. To do so helps to make the intentions of the research clear. It is possible
to formulate questions using different words, such as, ‘who’, ‘when’, ‘where’,
‘which’, ‘how many’ or ‘how much’. While questions that begin with such
words may appear to have different intentions, they are all versions of a ‘what’
question: ‘What individuals …’, ‘At what time …’, ‘At what place …’, ‘In what
situations …’, ‘In what proportion …’ and ‘To what extent …’. Similarly, some
questions that begin with ‘what’ are actually ‘why’ questions. For example,
‘What makes people behave this way?’ seeks an explanation rather than descrip-
tion. It needs to be reworded as: ‘Why do people behave this way?’.
Each research objective requires the use of a particular type of research ques-
tion or, in a few cases, two types of questions. Most research objectives require
‘what’ questions: exploration, description, prediction, evaluation and impact
assessment. It is only the objectives of understanding and explanation, and pos-
sibly evaluation and impact assessment, that require ‘why’ questions. ‘How’
questions are only used with the objective of change (see Table 1.1). Returning
to our two research questions, the first is a ‘what’ question that seeks a descrip-
tive answer, and the second is a ‘why’ question that asks for an explanation.
The Role of Hypotheses
It is a commonly held view that research should be directed towards testing
hypotheses. While some types of social research involve the use of hypotheses,
in a great deal of it hypotheses are either unnecessary or inappropriate. Clearly
stated, hypotheses can be extremely useful in helping to find answers to ‘why’
questions. In fact, it is difficult to answer a ‘why’ question without having some
ideas about where to look for the answer. Hence, hypotheses provide possible
answers to ‘why’ questions.
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In some types of research, hypotheses are developed at the outset to give this
direction; in other types of research, the hypotheses may evolve as the research
proceeds. When research starts out with one or more hypotheses, they should
ideally be derived from a theory of some kind, preferably expressed in the form
of a set of propositions. Hypotheses that are plucked out of thin air, or are just
based on hunches, usually make limited contributions to the development of
knowledge because they are unlikely to connect with the existing state of
knowledge.
Hypotheses are normally not required to answer ‘what’ questions. Because
‘what’ questions seek descriptions, they can be answered in a relatively straight-
forward way by collecting relevant data. For example, a question such as ‘What
is the extent of recycling behaviour among university students?’ requires spec-
ification of what behaviour will be included under ‘recycling’ and how it will be
measured. While previous research and even theory may help us decide what
behaviour is relevant to this concept, there is no need to hypothesize about the
extent of this behaviour in advance of the research being undertaken. The data
that are collected will answer the question. On the other hand, to answer the
question ‘Why are some students regular recyclers?’ it would be helpful to have
a possible answer to test, that is, a hypothesis.
This theoretical use of hypotheses should not be confused with their statisti-
cal use. The latter tends to dominate books on research methods and statistics.
As we shall see later, a great deal of research is conducted using samples that
are drawn from much larger populations. There are many practical benefits in
doing this. If such samples are drawn using statistically random procedures, and
if the response rate is very high, a researcher may want to generalize the results
found in a sample to the population from which the sample was drawn. Statis-
tical hypotheses perform a role in this generalization process, in making deci-
sions about whether the characteristics, differences or relationships found in a
sample can be expected to also exist in the population. Such hypotheses are not
derived from theory and are not tentative answers to research questions. Their
function is purely statistical. When research is conducted on a population or a
non-random sample, there is no role for statistical hypotheses. However, theo-
retical hypotheses are relevant in any research that requires ‘why’ questions to
be answered.
14
Table 1.1 Research questions and objectives
Research questions
Research objectives What Why How
Exploration ü
Description ü
Explanation ü
Understanding ü
Prediction ü
Intervention ü
Evaluation ü ü
Assess impacts ü ü
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What are Data?
In the context of social research, the concept of data is generally treated as
being unproblematic. It is rare to find the concept defined and even rarer to
encounter any philosophical consideration of its meaning and role in research.
Data are simply regarded as something we collect and analyze in order to arrive
at research conclusions.
The concept is frequently equated with the notion of ‘empirical evidence’,
that is, the products of systematic ‘observations’ made through the use of the
human senses. Of course, in social research, observations are made mainly
through the use of sight and hearing.
The concept of observation is used here in its philosophical sense, that is, as
referring to the use of the human senses to produce ‘evidence’ about the
‘empirical’ world. This meaning needs to be distinguished from the more spe-
cific usage in social research where it refers to methods of data collection that
use the sense of sight. In this latter method, ‘looking’ is distinguished from
other major research activities such as ‘listening’, ‘conversing’, ‘participating’,
‘experiencing’, ‘reading’ and ‘counting’. All of these activities are involved in the
philosophical meaning of ‘observing’.
Observations in all sciences are also made with the use of instruments,
devices that extend the human senses and increase their precision. For exam-
ple, a thermometer can measure temperature far more precisely and consis-
tently than can the human sense of touch. Its construction is based on notions
of hot and cold, more and less, and of an equal interval scale. In short, it has
built into it many assumptions and technical ideas that are used to extend dif-
ferences that can be experienced by touch. Similarly, an attitude scale, consist-
ing of an integrated set of statements to which responses are made, provides a
more precise and consistent measure than, say, listening to individuals dis-
cussing some issue.
The notion of empirical evidence is not as simple as it might seem. It entails
complex philosophical ideas that have been vigorously contested. These dis-
agreements centre on different claims that are made about:
• what can be observed;
• what is involved in the act of observing;
• how observations are recorded;
• what kinds of analysis can be done on them; and
• what the products of these observations mean.
There are a number of important and related issues involved in the act of
observing. One concerns assumptions that are made about what it is that we
observe. A second issue has to do with the act of observing, with the connec-
tion between what impinges on the human senses and what it is that produces
those impressions. A third issue is concerned with the role of the observer in
the process of observing. Can reality be observed directly or can we only
observe its ‘surface’ features? Is it reality that we observe, or do we simply
15
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process some mental construction of it? Does what we observe represent what
actually exists, or, in the process of observing, do we have to interpret the physi-
cal sensations in order to make them meaningful? Can we observe objectively,
that is, without contaminating the impressions received by our senses, or does
every act of observing also involve a process of interpretation? These are the
kinds of complex issues that lie behind the generation of data. Consciously or
unconsciously, every social researcher takes a stand on these issues. The posi-
tion adopted is likely to be that of the particular research tradition or paradigm
within which the researcher has been socialized and/or has chosen to work.
The issue of ‘objectivity’ is viewed differently in these research traditions. In
some traditions it is regarded as an ideal towards which research should strive. It
is assumed that a conscientious and well-trained researcher can achieve a satisfac-
tory level of objectivity. The ‘problem’ of objectivity is dealt with by establishing
rules for observing, for collecting data. In other traditions, ‘objectivity’ is regarded
as not only being unattainable but also as being meaningless. In these traditions,
the emphasis is on producing ‘authentic’ accounts of the social reality described by
social actors rather than accurate representations of some external reality.
Collecting any kind of data involves processes of interpretation. We have to
‘recognize’ what we see, we have to ‘know’ what it is an example of, and we
may have to ‘relate’ it to or ‘compare’ it with other examples. These activities
require the use of concepts, both lay and technical, and whenever we use con-
cepts we need to use meanings and definitions. For example, if we identify a
particular interaction episode as involving conflict, the observer needs to have a
definition of conflict and to be able to recognize when a sequence of behaviour
fits with the definition. Incidents of conflict do not come with labels attached;
the observer (with technical concepts) or, perhaps, the participants (with lay
concepts) must do the labelling. Defining concepts and labelling social activities
are interpretative processes that occur against the background of the observer’s
assumptions and prior knowledge and experiences. Data collected about, say,
the frequency of conflict between parents and children will have been ‘manu-
factured’ by a particular researcher. While a researcher may follow rules, crite-
ria and procedures that are regarded by her research community as being
appropriate, such rules etc. are simply agreements about how research should
be done and cannot guarantee ‘pure’ uncontaminated data. What they can
achieve is comparable data between times, places and researchers.
Data and Social Reality
All major research traditions regard data as providing information about some
kind of social phenomenon, and an individual datum as relating to some aspect
of that phenomenon. Just what the relationship is between the data and the
phenomenon depends to a large extent on the assumptions that are made about
the nature of social reality, that is, the ontological assumptions. In turn, the pro-
cedures that are considered to be appropriate for generating data about that
phenomenon depend on the assumptions that are made about how that social
reality can be known, that is, the epistemological assumptions.
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One major research tradition assumes that social reality is external to the
people involved: that it is the context in which their activities occur; and that
it has the capacity to constrain their actions. Knowledge of this reality can be
obtained by establishing a bridge to it by the use of concepts and their mea-
surement. Concepts identify aspects of the reality and instruments are designed
to collect data relevant to the concepts. In this way, data are supposed to rep-
resent aspects of, or what is going on in, some part of reality. Only those aspects
that can be measured are regarded as relevant to research. This tradition is asso-
ciated with positivism and critical rationalism, and its data-gathering proce-
dures are mainly quantitative.
A second research tradition adopts different ontological assumptions. In this
case, reality is assumed to consist of layers or domains. The ‘surface’ or empiri-
cal layer can be observed in much the same way as the tradition just described.
However, reality also has an ‘underlying’ layer that cannot usually be observed
directly. This is the ‘real’ layer consisting of the structures and mechanisms that
produce the regularities that can be observed on the surface. Knowledge of this
‘real’ layer can only be gained by constructing imaginary models of how these
structures and mechanisms might operate. Then, knowing what kinds of things
are worth looking for, painstaking research will hopefully produce evidence for
their existence, and perhaps will eventually expose them to the surface layer.
This position is known as scientific realism, and it uses a variety of quantitative
and qualitative data-gathering procedures.
A third major research tradition adopts yet another set of ontological assump-
tions. Social reality is regarded as a social construction that is produced and
reproduced by social actors in the course of their everyday lives. It consists of
intersubjectively shared, socially constructed meaning and knowledge. This
social reality does not exist as an independent, objective world that stands apart
from social actors’ experience of it. Rather, it is the product of the processes by
which social actors together negotiate the meanings of actions and situations. It
consists of mutual knowledge – meanings, cultural symbols and social institu-
tions. Social reality is the symbolic world of meanings and interpretations. It is
not some ‘thing’ that may be interpreted in different ways; it is those interpre-
tations. However, because these meanings are intersubjective, that is, they are
shared, they both facilitate and constrain social activity. With these ontological
assumptions, knowledge of social reality can only be achieved by collecting
social actors’ accounts of their reality, and then redescribing these accounts in
social scientific language. This position is known as interpretivism or social con-
structionism, and its data-gathering procedures are mainly qualitative.
This book is concerned with the first of these traditions.
Types of Data
An important issue in social research is the extent to which a researcher is
removed from the phenomenon under investigation. Any ‘observer’ is, by defi-
nition, already one step removed from any social phenomenon by dint of the
fact of viewing it from the ‘outside’. This means that the processes involved in
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‘observing’ require degrees of interpretation and manipulation. Even data
generated first-hand by a researcher have already been subjected to some pro-
cessing. As we have seen, there is no such thing as ‘pure’ data. However, not all
data are first-hand. A researcher may use data that have been collected by some-
one else, either in a raw form or analyzed in some way. Hence, social research
can be conducted that is more than one step removed from the phenomenon.
This notion of distance from the phenomenon can be categorized into three
main types: primary, secondary and tertiary. Primary data are generated by a
researcher who is responsible for the design of the study and the collection,
analysis and reporting of the data. These ‘new’ data are used to answer specific
research questions. The researcher can describe why and how they were col-
lected. Secondary data are the raw data that have already been collected by
someone else, either for some general information purpose, such as a govern-
ment census or another official purpose, or for a specific research project. In
both cases, the purpose in collecting such data may be different from that of
the secondary user, particularly in the case of a previous research project.
Tertiary data have been analyzed by either the researcher who generated them
or an analyst of secondary data. In this case the raw data may not be available,
only the results of this analysis.
While primary data can come from many sources, they are characterized by
the fact that they are the result of direct contact between the researcher and
the source, and that they have been generated by the application of particular
methods by the researcher. The researcher, therefore, has control of the pro-
duction and analysis, and is in a position to judge their quality. This judgement
is much more difficult with secondary and tertiary data.
Secondary data can come from the same kind of sources as primary data; the
researcher is just another step removed from it. The use of secondary data is
often referred to as secondary analysis. It is now common for data sets to be
archived and made available for analysis by other researchers. Such data sets
constitute the purest form of secondary data. Most substantial surveys have
potential for further analysis because they can be interrogated with different
research questions.
Secondary information consists of sources of data and other information collected
by others and archived in some form. These sources include government reports,
industry studies, archived data sets, and syndicated information services as well as
traditional books and journals found in libraries. Secondary information offers rela-
tively quick and inexpensive answers to many questions and is almost always the
point of departure for primary research. (Stewart and Kamis, 1984: 1)
While there are obvious advantages in using secondary data, such as savings
in time and cost, there are also disadvantages. The most fundamental drawback
stems from the fact that this previous research was inevitably done with dif-
ferent aims and research questions. It may also have been based on assump-
tions, and even prejudices, which are not readily discernible, or which are
inconsistent with those a researcher wishes to pursue. Secondly, there is the
possibility that not all the areas of interest to the current researcher may have
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been included. Thirdly, the data may be coded in an inconvenient form.
Fourthly, it may be difficult to judge the quality of secondary data; a great deal
has to be taken on faith. A fifth disadvantage for some research stems from the
fact that the data may be old. There is always a time lag between collection and
reporting of results, and even longer before researchers are prepared to archive
their data sets. Even some census data may not be published until at least two
years after they were collected. However, this time lag may not be a problem
in historical, comparative or theoretical studies.
With tertiary data, the researcher is even further removed from the social
world and the original primary data. Published reports of research and officially
collected ‘statistics’ invariably include tables of data that have summarized, cat-
egorized or have involved the manipulation of raw data. Strictly speaking, most
government censuses report data of these kinds, and access to the original data
set may not be possible. When government agencies or other bodies do their
own analysis on a census, they produce genuine tertiary data. Because control
of the steps involved in moving from the original primary data to tertiary data
is out of the hands of the researcher, such data must be treated with caution.
Some sources of tertiary data will be more reliable than others. Analysts can
adopt an orientation towards the original data, and they can be selective in what
is reported. In addition, there is always the possibility of academic fraud. The
further a researcher is removed from the original primary data, the greater the
risk of unintentional or deliberate distortion.
The purpose of this classification is to sensitize the researcher to the nature
of the data being used and its limitations. This discussion brings us back to the
key issue: what are data? In particular, it highlights the problem of the gap
between the researcher and the social phenomenon that is being investigated.
There is an interesting relationship between types of data and ontological
assumptions. Such assumptions about the nature of the reality being investi-
gated will not only have a bearing on what constitutes data but also determine
how far a researcher is seen to be removed from that reality. This can be illus-
trated with reference to the operation of stock markets. All major stock markets
in the world produce a numerical indicator that is used to follow movements in
that particular market. For example, the New York stock exchange uses the
Dow Jones index, the London exchange uses the FTSE 100, and the Tokyo
exchange the Nikkei. The share prices of a selection of stocks are integrated
into a summary number. This number or indicator is used to measure the
behaviour of ‘the market’. Trends can be calculated and, perhaps, models and
theories developed about cycles or stages in these trends.
But what kind of data are these indices? The answer to this question depends
on what view of reality is adopted. The notion of ‘the market’ is an abstract idea
that can refer to an entity that exists independently of the people who buy and
sell shares. Analysts frequently attribute the market with human or animal quali-
ties: it has ‘sentiments’, it ‘looks for directions’, it acts like a bull or a bear. Hence,
‘the market’ can be regarded as constituting an independent reality. From these
assumptions, the market indicator might be regarded as primary data; it measures
the behaviour of ‘the market’. The share prices are the raw data.
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Another (albeit much less common) set of assumptions would be to regard
the worldviews and behaviour of the people who buy and sell shares as consti-
tuting the basic social phenomenon. The decisions and actions of these people
generate the fluctuating prices of shares. The stockbrokers through whom these
people conduct their share transactions are equivalent to researchers who then
feed the outcomes of the decisions of these people into a particular market’s
database from which the price of any shares, at any time, can be determined
and trends plotted. Other researchers then take these average prices and do
some further analysis to produce a share price index. Further researchers can
then use the changes in the index to trace movements in ‘the market’. There-
fore, the price that individual investors pay for their parcel of shares is equiva-
lent to primary data, the closing or average price of the shares in any particular
company represents secondary data, and the share price index represents
tertiary data.
This example illustrates two things. First, it shows that how data are viewed
depends on the ontological assumptions about the social phenomenon being
investigated. Second, it shows that what is regarded as reality determines what
types of data are used. Reality can be either a reified abstraction, such as ‘the
market’, or it can be the interpretations and activities of particular social actors,
such as investors. Movements in a share price index can mean different things
depending on the assumptions that are adopted. It can be a direct, primary
measure of a particular reality, or it can be an indirect, tertiary measure of a
different kind of reality. Hence, knowing what data refer to, and how they
should be interpreted, depends on what is assumed as being the reality under
investigation, and the type of data that are being used.
Forms of Data
Social science data are produced in two main forms, in numbers or in words.
This distinction is usually referred to as either quantitative or qualitative data.
There seems to be a common belief among many researchers, and consumers of
their products, that numerical data are needed in scientific research to ensure
objective and accurate results. Somehow, data in words tend to be regarded as
being not only less precise but also less reliable. These views still persist in many
circles, even although non-numerical data are now more widely accepted. As
we shall see shortly, the distinction between words and numbers, between quali-
tative and quantitative data, is not a simple one.
It can be argued that all primary data start out as words. Some data are
recorded in words, they remain in words throughout the analysis, and the find-
ings are reported in words. The original words will be transformed and mani-
pulated into other words, and these processes may be repeated more than once.
The level of the language will change, moving from lay language to technical
language. Nevertheless, throughout the research, the medium is always words.
In other research, the initial communication will be transformed into numbers
immediately, or prior to the analysis. The former involves the use of pre-coded
response categories, and the latter the post-coding of answers or information
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provided in words, as in the case of open-ended questions in a questionnaire.
Numbers are attached to both sets of categories and the subsequent analysis
will be numerical. The findings of the research will be presented in numerical
summaries and tables. However, words will have to be introduced to interpret
and elaborate the numerical findings. Hence, in quantitative studies, data nor-
mally begin in words, are transformed into numbers, are subjected to different
levels of statistical manipulation, and are reported in both numbers and words;
from words to numbers and back to words. The interesting point here is whose
words were used in the first place and what process was used to generate them.
In the case where responses are made into a predetermined set of categories,
the questions and the categories will be in the researcher’s words; the respon-
dent only has to interpret both. However, this is a big ‘only’. As Foddy (1993)
and Pawson (1995, 1996) have pointed out, this is a complex process that
requires much more attention and understanding than it has normally been
given.
Sophisticated numerical transformations can occur as part of the analysis
stage. For example, responses to a set of attitude statements, in categories rang-
ing from ‘strongly agree’ to ‘strongly disagree’, can be numbered, say, from 1 to
5. The direction of the numbering will depend on whether a statement expresses
positive or negative attitudes on the topic being investigated, and on whether
positive attitudes are to be given high or low scores. Subject to an appropriate
test, these scores can be combined to produce a total score. Such scores are well
removed from the respondent’s original reading of the words in the statements
and the recording of a response in a category with a label in words.
So far, this discussion of the use of words and numbers has been confined to
the collection of primary data. However, these kinds of manipulations may have
already occurred in secondary data, and will certainly have occurred in tertiary
data.
The controversial issue in all of this is the effect that any form of manipulation
has on the relationship of the data to the reality it is supposed to measure. If all
observation involves interpretation, then some kind of manipulation is involved
from the very beginning. Even if a conversation is recorded unobtrusively, any
attempt to understand what went on requires the researcher to make interpreta-
tions and to use concepts. How much manipulation occurs is a matter of choice.
A more important issue is the effect of transforming words into numbers.
Researchers who prefer to remain qualitative through all stages of a research
project may argue that it is bad enough to take lay language and manipulate it
into technical language without translating either of them into the language of
mathematics. A common fear about such translations is that they end up dis-
torting the social world out of all recognition, with the result that research
reports based on them become either meaningless or, possibly, dangerous if
acted on.
The reason for this extended discussion of issues involved in transforming
words into numbers is to highlight the inherent problems associated with inter-
preting quantitative data and, hence, its analysis. Because of the steps involved
in transforming some kind of social reality into the language of mathematics,
and the potential for losing the plot along the way, the interpretation of the
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results produced by quantitative analysis must be done with full awareness of
the limitations involved.
Concepts and Variables
It is conventional practice to regard quantitative data as consisting of variables.
These variables normally start out as concepts, coming from either research
questions or hypotheses. First, it is necessary to define the concept in terms of
the meaning it is to have in a particular research project. For example, age might
be defined as ‘years since birth’, and education as ‘the highest level of formal
qualification obtained’. Unless there is some good reason to do otherwise, it is
good practice to employ a definition already in use in that particular field of
research. In this way, results from different studies can be easily compared.
The second step is to operationalize the concept to show how data related to
it will be generated. This requires the specification of the procedures that will
be used to classify or measure the phenomenon being investigated. For exam-
ple, in order to measure a person’s age, it is necessary either to ask them or to
obtain the information from some kind of record, such as a birth certificate.
Similarly, with education, you can either ask the person what their highest
qualification is, or you can refer to appropriate documents or records. The way
a concept is defined and measured has important consequences for the kinds of
data analysis that can be undertaken.
The idea behind a variable is that it can have different values, that characteris-
tics of objects, events or people can be measured along some continuum that
forms a uniform numerical scale. This is the nature of metric measurement. For
example, age (in years) and attitudes towards some object (in scores) are vari-
ables. However, other kinds of characteristics, such as religion, do not share this
property. They are measured in terms of a set of different categories. Something
can be identified as being in a particular category (e.g. female), but there is no
variation within the category, only differences between categories (e.g. males
and females). As there is no variability within such categories, the results of such
measurement are not strictly variables. They could be called variates, but this
concept also has another meaning in statistics. Therefore, I shall follow the
established convention of referring to all kinds of quantitative measurement as
variables. It is to the different kinds or levels of measurement that we now turn.
Levels of Measurement
In quantitative research, aspects of social reality are transformed into numbers
in different ways. Measurement is achieved either by the assignment of objects,
events or people to discrete categories, or by the identification of their charac-
teristics on a numerical scale, according to arbitrary rules. The former is
referred to here as categorical measurement and the latter as metric measure-
ment. Within these levels of measurement are two further levels: nominal and
ordinal, and interval and ratio, respectively.
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Categorical Measurement
Everyday life would be impossible without the use of numbers. However, using
numbers does not mean that we need to use complex arithmetic or mathemat-
ics. Frequently, numbers are simply used to identify objects, events or people.
Equipment and other objects are given serial numbers or licence numbers so that
they can be uniquely identified. Days of the month and the years of a millen-
nium are numbered in sequence. The steps involved in assembling an object are
numbered. People who make purchases in a shop can be given numbers to ensure
they are served in order. In none of these examples are the numbers manipu-
lated; they are simple used as a form of identification, and, in some cases, to
establish an order or sequence. The alphabet could just as easily be used, and
sometimes is, except that it is much more restricted than our usual number
system as the latter has no absolute limit. This elementary way of using numbers
in real life and in the social sciences is known as categorical measurement.
As has already been implied, categorical measurement can be of two types.
One involves assigning numbers to categories that identify different types of
objects, event or people; in the other, numbers are used to establish a sequence
of objects, events or people. Categories can either identify differences or they
can be ordered along some dimension or continuum. The former is referred to
as nominal-level measurement, and the latter as ordinal-level measurement.
Nominal-level measurement
In nominal-level measurement, the categories must be homogeneous, mutually
exclusive and exhaustive. This means that all objects, events or people allocated
to a particular category must share the same characteristics, they can only be
allocated to one category, and all of them can be allocated to some category in
the set. The categories have no intrinsic order to them, as is the case for the
categories of gender or religion. People can also be assigned numbers arbitrarily
according to some criterion, such as different categories of eye colour – blue
(1), brown (2), green (3), etc. However, these categories have no intrinsic order
(except, of course, on the colour spectrum).
Ordinal-level measurement
The same conditions apply in ordinal-level measurement, with the addition that
the categories are ordered along some continuum. For example, people can be
assigned numbers in terms of the order in which they cross the finishing line in
a race, they can be assigned social class categories (‘upper’, ‘middle’ and ‘lower’)
according to their income or occupational status, or they can be assigned to
age categories (‘old’, ‘middle-aged’ and ‘young’) according to some criterion.
A progression or a hierarchy is present in each of these examples.
However, the intervals between such ordinal categories need not be equal.
For example, the response categories of ‘often’ (1), ‘occasionally’ (2) and
‘never’ (3) cannot be assumed to be equally spaced by researchers, because it
cannot be assumed that respondents regard them this way. When the numbers
in brackets are assigned to these categories, they only indicate the order in the
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sequence, not how much of a difference there is between these categories.
They could just as easily have been identified with ‘A’, ‘B’ and ‘C’, and these
symbols certainly do not imply any difference in magnitude.
Similarly, the commonly used Likert categories for responses to attitude
statements, ‘strongly agree’, ‘agree’, ‘neither agree nor disagree’, disagree’, and
‘strongly disagree’, are not necessarily evenly spaced along this level of agree-
ment continuum, although researchers frequently assume that they are. When
this assumption is introduced, an ordinal-level measure becomes an interval-
level measure with discrete categories.
Metric Measurement
There are more sophisticated ways in which numbers can be used than those
just discussed. The introduction of the simple idea of equal or measurable inter-
vals between positions on a continuum transforms categorical measurement
into metric measurement. Instead of assigning objects, events or people to a
set of categories, they are assigned a number from a particular kind of scale of
numbers, with equal intervals between the positions on the scale. For example,
we measure a person’s height by assigning a number from a measuring scale. We
measure intelligence by assigning a person a number from a scale that repre-
sents different levels of intelligence (IQ). Of course, with categorical measure-
ment, it is necessary to have or to create a set of categories into which whatever
is being measured can be assigned. However, these categories do not have any
numerical relationships and, therefore, cannot have the rules of a number
system applied to them.
Hence, the critical step in this transition from categorical to metric mea-
surement is the mapping of the things being measured onto a scale. The scale
has to exist, or be created, before the measurements are made, and these scales
embody the properties and rules of a number system. Measuring a person’s
height clearly illustrates this. You have to have a measuring instrument, such as
a long ruler or tape measure, before a person’s height can be established. We
can describe people as being ‘tall’, ‘average’ or ‘short’. Such ordinal-level cate-
gories allow us to compare people’s height only in very crude terms. Adding
numbers to the categories, say ‘1’, ‘2’ and ‘3’, neither adds precision to the mea-
surement nor does it allow us to assume that the intervals between the cate-
gories are equal. Alternatively, we could line up a group of people, from the
tallest to the shortest, and give them numbers in sequence. Each number simply
indicates where a person is in the order and has nothing to do with the actual
magnitude of their height. In addition, the differences in height between neigh-
bouring people will vary and the number assigned to them will not indicate this.
However, once we stand them beside a scale in, say, centimetres, we can get a
measure of magnitude, and because they are all measured against the same scale
we can make precise comparisons between any members of the group. Preci-
sion of measurement is only one of the considerations here. The important
change is that much more sophisticated forms of analysis can now be used
which, in turn, means that more sophisticated answers can be given to research
questions.
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All metric scales of measurement are human inventions. The way in which
points on the scale are assigned numbers, the size of the intervals between those
points, whether or not there are gradations between these points, and where
the numbering starts, are all arbitrary. Scales differ in how the zero point is
established. Some scales have an absolute or true zero, while for others there is
no meaningful zero, that is, the position of zero is arbitrary.
Interval-level measurement
Interval-level measurement is achieved when the categories or scores on a scale
are the same distance apart. Whereas in ordinal-level measurement the num-
bers ‘1’, ‘2’ and ‘3’ only indicate relative position, say in finishing a race, in
interval-level measurement, the numbers are assumed to be the same distance
apart – the interval between ‘1’ and ‘2’ is the same as the interval between
‘2’ and ‘3’. As the numbers are equally spaced on the scale, each interval has the
same value.
The distinguishing feature of interval-level measurement is that the zero is
arbitrary. Whatever is being measured cannot have a meaningful zero value. For
example, an attitude scale may have possible scores that range from 10 to 50.
Such scores could have been derived from an attitude scale of ten items, using
five response categories (from ‘strongly agree’ to ‘strongly disagree’) with the
categories being assigned numbers from 1 to 5 in the direction appropriate to
the wording (positive or negative) of the item.2
However, these scores could
just as easily have ranged from 0 to 40 (with categories assigned numbers from
0 to 4) without altering the relative interval between any two scores. In this
case, a zero score is achieved by an arbitrary decision about what numbers to
assign to the response categories. It makes no sense to speak of a zero attitude,
only relatively more positive or negative attitudes.
Ratio-level measurement
Ratio-level measurement is the same as interval-level measurement except that
it has an absolute or true zero. For example, goals scored in football, or age in
years, both have absolute or true zeros; it is possible for a team to score no goals,
and a person’s age is normally calculated from the time of birth – point zero.
Ratio-level measurement is not common in the social sciences and is limited
to examples such as age (in years), education (in years) and income (in dollars
or other currencies). This level of measurement has only a few advantages over
the interval level of measurement, mainly that statements such as ‘double’ or
‘half’ can be made. For example, we can say that a person aged 60 years is twice
as old as a person aged 30 years, or that an income of $20,000 is only half that
of $40,000. These kinds of statements cannot be made with interval-level vari-
ables. For example, with attitude scales, such as those discussed above, it is not
legitimate to say that one score (say 40) is twice as positive as another (say 20).
What we can say is that one score is higher, or lower, than another by so many
scale points (a score of 40 is 10 points higher than a score of 30, and the latter
is 10 points higher than a score of 20) and that an interval of, say 10 points, is
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the same anywhere on the scale. The same applies to scales used to measure
temperature. Because the commonly used temperature scales, Celsius and
Fahrenheit, both have arbitrary zeros, we cannot say that a temperature of 30°C
is twice as hot as 15°C, but the interval between 15°C and 30°C is the same as
that between 30°C and 45°C. Similarly, not only is 30°C a different temperature
than 30° Fahrenheit, but an interval of 15° is different on each scale. However,
as the kelvin scale does have a true zero, the absolute minimum temperature
that is possible, a temperature of 400K is twice as hot as 200K.
Compared to ratio-level measurement, it is the arbitrary zero that creates the
limitations in interval-level measurement. In most social science research, this
limitation is not critical; interval-level measurement is usually adequate for
most sophisticated forms of analysis. However, we need to be aware of the
limitations and avoid drawing illegitimate conclusions from interval-level data.
Discrete and Continuous Measurement
Metric scales also differ in terms of whether the points on the scale are discrete
or continuous. A discrete or discontinuous scale usually has units in whole
numbers and the intervals between the numbers are usually equal. Arithmetical
procedures, such as adding, subtracting, multiplying and dividing, are permissi-
ble. On the other hand, a continuous scale will have an unlimited number of
possible values (e.g. fractions or decimal points) between the whole numbers.
An example of the former is the number of children in a family and, of the latter,
a person’s height in metres, centimetres, millimetres, etc. We cannot speak of
a family having 1.8 children (although the average size of families in a country
might be expressed in this way), but we can speak of a person being 1.8 metres
in height. When continuous scales are used, the values may also be expressed
in whole numbers due to rounding to the nearest number.
Review
The characteristics of the four levels of measurement are summarized in Table 1.2.
They differ in their degree of precision, ranging from the least precise (nominal)
to the most precise (ratio). The different characteristics, and the range of
precision, mean that different mathematical procedures are appropriate at each
level. It is too soon to discuss these differences here; they will emerge through-
out Chapters 3–6.
However, a word of caution is appropriate. It is very easy to be seduced by
the precision and sophistication of interval-level and ratio-level measurement,
regardless of whether they are necessary or theoretically and philosophically
appropriate. The crucial question is what is necessary in order to answer the
research question under consideration. This relates to other aspects of social
research, such as the choice of data sources, the method of selection from these
sources and the method of data collection. The latter, of course, will have a con-
siderable bearing on the type of analysis that can and should be used. In quan-
titative research, the choice of level of measurement at the data-collection
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stage, and the transformations that may be made, including data reduction, will
determine the types of analysis that can be used.
Finally, it is important to note that some writers refer to categorical data as
qualitative and metric data as quantitative. This is based on the idea that quali-
tative data lack the capacity for manipulation other than adding up the number
in the categories and calculating percentages or proportions. This usage is not
adopted here. Rather, ‘qualitative’ and ‘quantitative’ are used to refer to data in
words and numbers, respectively. Categorical data involve the use of numbers
and not words, allowing for simple numerical calculations. According to the
definitions being used here, categorical data are clearly quantitative.
Transformations between Levels of Measurement
It is possible to transform metric data into categorical data but, in general, not the
reverse. For example, in an attitude scale, scores can be divided into a number of
ranges (e.g. 10–19, 20–29, 30–39, 40–50) and labels applied to these categories
(e.g. ‘low’, ‘moderate’, ‘high’ and ‘very high’). Thus, interval-level data can be
transformed into ordinal-level data. Something similar could be done with age (in
years) by creating age categories that may not cover the same range, say, 20–24,
25–34, 35–54, 55+. In this case, the transformation is from ratio level to ordinal.
While such transformations may be useful for understanding particular variables,
and relationships between variables, measurement precision is lost in the process,
and the types of analysis that can be applied are reduced in sophistication. It is
important to note, however, that if a range of ages or scores is grouped into cate-
gories of equal size, for example, 20–29, 30–39, 40–49, 50–59, 60–69, etc., the
categories can be regarded as being at the interval level; they cover equal age inter-
vals, thus making their midpoints equal distances apart. All that has changed is the
unit of measurement, in 10-year age intervals rather than 1-year intervals.
27
Table 1.2 Levels of measurement
Level Description Types of categories Examples
Nominal A set of categories for Categories are homogeneous, Marital status
classifying objects, events or mutually exclusive and Religion
people, with no assumptions exhaustive. Ethnicity
about order.
Ordinal As for nominal-level Categories lie along a Frequency (often,
measurement, except the continuum but the distances sometimes, never)
categories are ordered between them cannot be Likert scale
from highest to lowest. assumed to be equal.
Interval A set of ordered and equal- Categories may be discrete Attitude score
interval categories on a or continuous with arbitrary IQ score
contrived measurement scale. intervals and zero point. Celsius scale
Ratio As for interval-level Categories may be discrete Age
measurement or continuous but with an Income
absolute zero. No. of children
3055-ch01.qxd 1/10/03 10:37 AM Page 27

There are a few cases in which it is possible to transform lower-level
measurement to a higher level. For example, it is possible to take a set of nominal
categories, such as religious denomination, and introduce an order using a par-
ticular criterion. For example, religious categories could be ordered in terms of
the proportion of a population that adheres to each one, or, more complexly, in
terms of some theological dimension. Similarly for categories of political party
preference, although in this case dominant political ideology would replace
theology. In a way, such procedures are more about analysis than measurement;
they add something to the level of measurement used in order to facilitate the
analysis.
The reason why careful attention must be given to level of measurement in
quantitative research is that the choice of level determines the methods of
analysis that can be undertaken. Therefore, in designing a research project,
decisions about the level of measurement to be used for each variable need to
anticipate the type of analysis that will be required to answer the relevant
research question(s). Of course, for certain kinds of variables, such as gender,
ethnicity and religious affiliation, there are limited options. However, for other
variables, such as age and income, there are definite choices. For example, if age
is pre-coded in categories of unequal age ranges, then the analysis cannot go
beyond the ordinal level. However, if age was recorded in actual years, then
analysis can operate at the ratio level, and transformations also made to a lower
level of measurement. Such a simple decision at the data-collection stage can
have significant repercussions at the data-analysis stage. The significance of
the level of measurement for choice of method of analysis will structure the
discussion in Chapters 3–6.
What is Data Analysis?
All social research should be directed towards answering research questions
about characteristics, relationships, patterns or influences in some social pheno-
menon. Once appropriate data have been collected or generated, it is possible
to see whether, and to what extent, the research questions can be answered.
Data analysis is one step, and an important one, in this process. In some cases,
the testing of theoretical hypotheses, that is, possible answers to ‘why’ research
questions, is an intermediary step. In other cases, the research questions will be
answered directly by an appropriate method of analysis.
The processes by which selection is made from the sources of data can also
have a major impact on the choice of methods of data analysis. The major con-
sideration in selecting data is the choice between using a population and a sample
of some kind. If sampling is used, the type of data analysis that is appropriate
will depend on whether probability or non-probability sampling is used. Hence,
it is necessary to review briefly how and why the processes of selecting data
affect the choice of methods of data analysis.
28
3055-ch01.qxd 1/10/03 10:37 AM Page 28

Types of Analysis
Various methods of data analysis are used to describe the characteristics of
social phenomena, and to understand, explain and predict patterns in social life
or in the relationships between aspects of social phenomena. In addition, one
type of analysis is concerned with estimating whether characteristics and
relationships found in a sample randomly drawn from a population could also
be expected to exist in the population. Hence, analysis can be divided into four
types: univariate descriptive, bivariate descriptive, explanatory and inferential.
Univariate Descriptive Analysis
Univariate descriptive analysis is used to represent the characteristics of some
social phenomenon (e.g. student academic performance on a particular course).
This can be done in a number of ways:
• by counting the frequency with which some characteristic occurs (e.g. the
total marks3
students receive on a particular course);
• by grouping scores of a certain range into categories and presenting these
frequencies in pictorial or graphical form (e.g. student’s total marks);
• by calculating measures of central tendency (e.g. the mean marks obtained
by students on the course); and
• by graphing and/or calculating the spread of frequencies around this centre
point (e.g. plotting a line graph of the frequency with which particular
marks were obtained, or calculating a statistic that measures the dispersion
around the mean).
There are clearly many ways in which the phenomenon of student academic
performance can be described and compared. The principles of each of these
methods will be elaborated later in this chapter, and they will be illustrated in
later chapters.
Bivariate Descriptive Analysis
Bivariate descriptive analysis is a step along the path from univariate analysis to
explanatory analysis. It involves either establishing similarities or differences
between the characteristics of categories of objects, events or people, or describ-
ing patterns or connections between such characteristics.
Typically, patterns are investigated by determining the extent to which the
position of objects, events or persons on one variable coincides with their posi-
tion on another variable. For example, does the position of people on a measure
of height coincide with their position on a measure of weight? If the tallest
people are also the heaviest, and vice versa, then these two measures can be said
to be associated. Sometimes this is expressed in terms of whether position on
one measure is a good predictor of position on another measure, that is,
whether the height of people is a good predictor of their weight.
29
3055-ch01.qxd 1/10/03 10:37 AM Page 29

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asemalle, missä ne lastattiin junaan. Seuraavana päivänä valtasi
eskadroona Humaljoen ja Härkölän patterit. Huhtik. 27 p:nä
kuljetettiin eskadroona junalla Koivistolle, paitsi II joukkuetta, joka
jäi Humaljoen asemalle. Aamulla aikaisin alettiin ratsastus
pohjoiseen. Eskadroona kokoontui Peusan tienhaarassa, mistä
matkaa jatkettiin Rokkalanjoelle. Vahtimestari Lihtonen ratsasti
toisen joukkueen kanssa Kaislahden majataloon, minne oli määrä
toistaiseksi jäädä. Vahdit asetettiin. Kohta senjälkeen saapui
luutnantti Relander mukanaan kolme harhaan joutunutta hallituksen
joukkojen sotilasta. Näiden sekavat puheet tuottivat sangen ikäviä
seurauksia eskadroonalle. Ne näet johtivat meidät taisteluun noin
15-kertaista vihollista vastaan. Heti luutnantti Relanderin majataloon
saavuttua otettiin 12 vihollisen pakolaista vangiksi.
"Klo 12 päivällä kuului vahtiemme hälyytyslaukauksia. Kahdesti
lyötiin päällekäyvä vihollinen takaisin, mutta ylivoiman edestä täytyi
eskadroonan viimein vetäytyä takaisin Makslahteen, yöpyen siellä.
Taistelun vaatimat uhrit olivat lukumääräämme nähden sangen
raskaat. Luutnantti Brommels ja 10 miestä kaatui, 9 haavoittui ja 2
joutui vangiksi. Huhtikuun 29 päivänä aamulla lähti kornetti Salmio
joukkueensa kanssa partioon Rokkalaan. Sieltä jatkoi aliupseeri O.
Vinter 7 miehen kerä matkaa Uuraaseen, valloitti sen ja otti 300
vankia. Vahtimestari Lihtonen ratsasti joukkueensa kanssa Kaijalan
kylään ja vahtimestari Keränen Johanneksen kirkolle.
"Edellisenä päivänä Kaislahdessa kohtaamamme vihollinen ei
uskaltanutkaan käyttää meidän perääntymistämme hyväkseen, vaan
pakeni epäjärjestyksessä Uuraan salmen yli vieden vangit mukanaan.
Patrullimme toi kuitenkin miehemme pois, ottaen, kuten jo edellä on
sanottu, lukumääräänsä nähden suhteettoman suuren vankimäärän.
Tähän vaikutti nähtävästi se, että Viipuri oli jo silloin vallattu, joten

punaisilta oli jo kaikki toivo kadonnut, varsinkin kun huomasivat
pakotien rantapitäjienkin kautta olevan tukossa.
"Sotasaalista saimme Härkölän, Tuppuransaaren, Humaljoen,
Puumalan ja Himottulan pattereilta 45 kpl. 8—2 1/4 tuuman tykkiä, 4
suurta valonheittäjää, useita kymmeniä tuhansia tykinpanoksia,
useita etäisyyden mittaajia, öljy- ja sähkömoottoreita, konepajan,
paljon ruutia ja kiväärinpatruunoita, puhelimia y.m.
"Kun tähän vielä lisätään Inosta saatu suunnaton sotasaalis: pari
sataa tykkiä ja ainakin parin miljardin (!) arvosta muuta tavaraa, niin
on se kunnioitettava saalis muutamien päivien ja vähäisen joukon
osalle. Sitäpaitsi vapautettiin monta pitäjää punikkien vallasta; seutu
Terijoelta Uuraaseen asti oli valkoisten hallussa ja Karjalan
Kannaksen läntinenkin osa pääsi punaisesta painajaisestaan.
"Muuten lienee Terijoen valloittaminen ainoita harvoja tapauksia
Suomen vapaussodassa, jolloin taistelu ratkaistiin ratsuväki-atakilla!"
Karjalan Kannas oli valkoisten hallussa, vihollinen lyöty rajan taa,
josta so ei sen koommin enää tohtinut hävitysretkilleen Suomen
puolelle tulla ja ensi kertaa tunsi jokainen olevansa omassa
maassaan, omassa itsenäisessä, itsestään huoltapitävässä ja
kansansa vaalimassa maassa. Ylpeä ilo paisutti sydäntä sitä
ajatellessa! Olihan vuosisatainen unelma toteutunut, olihan
vihdoinkin selvä raja Suomen ja Venäjän välillä ja olivathan omat
pojat rajaa vartioimassa!
Julistuksessaan huhtik. 24 p. lausuu Suomen Tasavallan
sotajoukkojen Ylipäällikkö seuraavasti:

"Karjalan urhoolliset soturit! Joka kerta kun saavun Karjalan
rintamalle, voin tervehtiä teitä ja onnitella uusista suurista voitoista.
Uudenkirkon, Raivolan, Terijoen ja Rajajoen valloitus on katkaissut
viholliseltamme tien Pietariin. Viimeinen taistelu on vielä jäljellä.
Karjalan pääkaupungin ja samalla punaryssien viimeisen ja
vahvimman tukikohdan valloitus. Valtavaa ylivoimaa vastaan olette te
verellänne puolustaneet Karjalaa.
"Nyt kun käsky yli rintaman kuuluu: Eteenpäin Viipuriin!, ei löydy
sitä voimaa, joka voisi seistä tätä vastaan. Nyt lyö Suomen valkoinen
armeija ratkaisevan iskunsa ja kohta on liehuva Suomen lippu ensi
kertaa Viipurin linnan tornissa. Eteenpäin Suomen urhoollinen
armeija! Isänmaa seuraa teidän voittokulkuanne!
"Antreassa, huhtikuun 24 p. 1918.
Mannerheim."
Viipurin piiritys ja valloitus.
Edellä olen maininnut, että Viipurin kaupunkikin jo oli valkoisten
hallussa ja punaisten tuki ja turva silläkin taholla siis pettänyt. Kun
kuitenkin nämä tapahtumat, Viipurin piiritys ja valloitus, aivan kuin
kruunaavat valkoisen armeijan taistelut ja ponnistelut, niin lienee
paikallaan lyhyt selonteko niistäkin tässä yhteydessä.
Kuten jo ennemmin lyhyesti mainitsin, oli kenraalimajuri Tollin
hyökkäyssuunnitelma seuraava: eversti Ausfeldin ryhmä puhdistaa
kannaksen ja katkaisee yhteyden Pietariin, kenraalimajuri Wilkmanin
ryhmä hyökkää idästä ja etelästä Viipuriin ja valloittaa kaupungin

samaan aikaan kun everstiluutnantti Sihvon ryhmä tuhoaisi
vastustajansa Saimaasta Heinjoelle saakka.
Kenraalimajuri Wilkmanin joukot, joita jääkärieverstiluutnantti
Jernström johti eteläistä ja eversti v. Coler pohjoista eli Talin kautta
Viipuriin hyökkäävää osaa, valtasivat ankaran taistelun jälkeen
Kämärän kyliin ja yöllä klo 1.10 Sainion aseman. Seuraavana
aamuna, huhtikuun 21 päivänä, valtasivat eversti v. Colerin joukot
Talin aseman. Oikean sivustaryhmän tehtävänä oli pidättää vihollinen
asemissaan. Niinpä katkaisikin II Karjalan rykmentin XI pataljoonan
lähettämä komennuskunta räjäyttämällä radan Kavantsaaren ja
Karisalmen asemien välillä keskellä yötä huhtikuun 24 päivää vasten.
Mutta kun seuraavan päivän aamuna ryhdyttiin ratkaisuun s.t.s.
tuhoamaan vihollista, niin jättikin tämä kuukausien kuluessa vahvasti
varustamansa asemat ja pakeni päätä pahkaa Kilpeenjoen ja
Juustilan kautta Viipuriin. Vain muutamissa kohdin taisteli se
epätoivon vimmalla; muualla se sytytti talot ja varastot tuleen sekä
hajautui metsiin paeten täydellisessä epäjärjestyksessä.
Karjalan II ja III rykmentti suorittivat tänään ja seuraavina päivinä
odottamattoman suuret tehtävät. Tottuneina vain asemasotaan ja
melkein kokonaan puutteellisesti harjoitettuina ei niiltä voitu vaatia
marssikestävyyttä ja -kuntoa, mutta siitä huolimatta ne pystyivät
antamaan mestarinäytteen. III Karjalan rykmentti, jääkärimajuri
Sarlinin johdolla, valloitti Joutsenon ja marssi 26 päivän aamuna
Lappeenrantaan. II Karjalan rykmentti, murrettuaan punaisten
rintaman Pihkalanjärven kohdalta ja vallattuaan Kavantsaaren
aseman sekä Ahvolan ja Oravalan rintamavarustukset, marssi
Kilpeenjoen kautta Juustilaan karkoittaen sinne yöpyneet punaisten
jälkijoukot, joilla oli uhkana polttaa kaikki rakennukset seuraavana
aamuna lähtiessään.

Tämän päivän sotasaalis oli suuri siitä huolimatta, että punaryssät
ehtivät tuhoamaan huomattavan osan siitä. Erittäin mainitsemista
ansaitsee uudenaikainen panssarivaunu ja ampumatarvejuna
Kavantsaaren asemalla.
Jo 27 päivän aamuna valtasivat II Karjalan rykmentin joukot
Hovinmaan aseman ja ratsuväki ulotti tiedustelunsa aina rantaan
asti. Hitaammin kulkeva jalkaväki seurasi mukana vallaten 28
päivänä Naulasaaren betonivarustukset ja asettuen asemiin lännen
puolelle Viipuria.
Nyt oli Viipurin piiritys maan puolelta yhtenäinen, mutta
Suomenlahden rantaan lähetetty tykistö saapui, ikävä kyllä, paria
päivää liian myöhään estämään punaisten pakoa meritse.
Samaan aikaan valtasivat III Karjalan rykmentin joukot Simolan ja
Vainikkalan asemat taisteltuaan epätoivon vimmalla asemiaan
puolustavia punikkeja vastaan. Näiden taisteluiden onnelliseen
tulokseen vaikutti ratkaisevasti jääkärikapteeni Pippingin johtama
tykistö, joka kulki uhkarohkeasti kärjen mukana, joskus ennen
sitäkin.
Tällä aikaa supistivat eversti v. Colerin ja jääkärieverstiluutnantti
Jernströmin joukot vahvaa saartoketjuaan Viipurin itä- ja
eteläpuolella. Tykistön huolellisesti ohjattu tuli sytytti tulipaloja
esikaupungeissa ja aiheutti ankaria räjähdyksiä vihollisen
ampumatarve-varastoissa Kolikkoinmäellä. 28 päivänä seisoivat
valkoiset joukot jo Papulan lahden itärannalla Karjalan
kaupunginosassa ja varustautuivat hyökkäämään kaupunkiin,
saatuaan merkin etelästä käsin osittain palaneen Kolikkoinmäen
kautta kaupunkiin hyökkäävien joukkojen etenemisestä.

Yöllä 29 päivää vasten tapahtui sitten tuo kauan ja jännityksellä
odotettu Viipurin valtaus. Tykistövalmistelun jälkeen marssivat
valkoiset joukot vanhaan Torkkelin kaupunkiin ja miehittivät sen.
Punaset, joista jo iltayöstä oli suurin osa jättänyt kaupungin, eivät
pystyneet tekemään vastarintaa. Vain siellä täällä jokunen
yksityislaukaus kaikui yön hiljaisuudessa ja autioilla kaduilla kuului
kaameana valkoisten joukkojen vakava astunta.
Mutta Tienhaaran kautta pakoon pyrkiviä punaisia odottikin
epämieluinen yllätys: II Karjalan rykmentin joukot pitivät sitkeästi
puoliaan ja välittämättä moninkertaisesta ylivoimasta ja
epätoivoisesti taistelevasta vihollisesta pysyttivät ne asemansa!
Taistelu, joka alkoi klo 1/2 1 aikaan yöllä 29 päivää vasten punaisten
pyrkiessä Tienhaaran varustuksista kaikkiin suuntiin, kävi
kiivaimmaksi Naulasaaren varustusten luona ja Haminaan johtavan
tien varrella.
Jääkärikapteeni Salmisen, vänrikkien E. Heimolaisen ja S. Uskin
henkilökohtaiseksi ansioksi on luettava se, että vähäiset saartojoukot
pystyivät vastustamaan ja lopulta voittamaankin ylivoimaisen
vihollisen, joka klo 7 a.p. antautui menetettyään kaatuneina ja
haavoittuneina lähemmä tuhat miestä.
Paitsi joukon viidettätuhatta vankia, saatiin Tienhaaran luona
monta vaunua käsittävä uudenaikainen panssarijuna, kokonainen
kuormasto ja suuri joukko käyttökunnossa olevia tykkejä ja
konekiväärejä sekä runsaasti ampumavaroja.
Tienhaaran taistelun jälkeen oli Viipurin valloitus täydelleen
suoritettu ja punaisten viimeinen tuki ja turva otettu. Pohjois-
Hämeen kaksipataljoonainen rykmentti, joka oli reservinä seurannut
Jääskestä Juustilaan, sai nyt astua etulinjaan jääkärieverstiluutnantti

Mandelinin ollessa pakoitettu marssittamaan rykmenttinsä kesken
taistelua takaisin Juustilan kautta Papulaan. Vastusta kohtaamatta
kulki Pohjois-Hämeen rykmentti kaupunkiin.
III Karjalan rykmentti taisteli jääkärimajuri Sarlinin johdolla vielä
monta kiivasta ja kunniakasta taistelua marssien aina Haminan
porteille asti, mutta kertomus siitä kuuluu jo toisille.
Riemuiten marssivat valkoiset joukot Viipuriin! Talvisten taistojen
ja
pimeiden kuukausien unelmat ja toiveet olivat vihdoinkin täyttyneet!
Valkoisena valkeni Vapun päivä tänä vuonna! Valkoisena ja vapaana
Suomen vapautuksen päivä!
Yleiskatsaus.
Viimeinen punaisten tukikohta oli valloitettu. Suomen lippu liehui
Torkkelin linnan harjalla ja valkoinen armeija kiitti Korkeinta
kaitselmusta ulkoilma-jumalanpalveluksessa Viipurin urheilukentällä.
Suomen lakia ja järjestystä kunnioittava osa kansaa riemuitsi
valkoisen voiton johdosta ja siunasi maanpoveen painuneiden
sankarien muistoa sekä rukoili Luojan siunausta vielä eläville
vapaustaistelijoille. Valkoiset toiveet täyttivät jokaisen rinnan ja
vilpitön päätös työskennellä isänmaan ja kansan eteen kuvastui
kaikkien katseista. Vain jokunen epäilijä rohkeni varovaisesti esitellä
mielipiteitään ja surupukuiset omaiset hautakumpuja vaiteliaina
koristivat.

Suuri muutos oli tapahtunut pimeän talven aikana: Suomen
maassa oli taattu työrauha, lain ja oikeuden turva! Suomen maa ja
kansa oli itsenäinen, vapaat — ikeensä alta noussut! Ja noussut
oman uskonsa voimalla! Sillä se apu, mikä ulkoapäin — Saksasta —
saatiin, olisi varmasti jäänyt tulematta, jollei Suomen kansan oma
usko oikeutensa voittoon olisi teettänyt niitä tekoja, jotka lopultakin
takasivat Suomen kansan voiman! Sitäkin suuremmalla syyllä
voimme pitää tätä seikkaa varmana, kun tiedämme, että omien
maanmiestemmekin — jääkärien — lähtö Saksasta Suomeen
auttamaan oli kyseenalaisena ja vain suurilla ponnistuksilla
saavutettu!
Ellei Saksan ylin sodanjohto — Hindenburg ja Ludendorff — olisi
nähnyt asioiden lopultakin ratkeavan valkoisen Suomen eduksi, ellei
se olisi katsonut omien etujensa mukaiseksi vielä viime hetkessä
tulla "auttamaan" Suomen kansaa, niin ei se olisi koskaan
nostattanut joukkojaan maihin Suomen rannoilla.
Näin hankki siis Suomen kansa oman kuntonsa uskolla senkin
tervetulleen avun. Taistelu Taavetin asemalla tammikuun 21 päivänä,
jossa taistelussa jääkäri L. Pelkonen Pyhäjärveltä (V. 1.) sai
surmansa kesken rohkeaa ja neuvokasta yritystään karkoittaa
punaiset käsikranaatilla asemarakennuksesta, sekä Karjalan ja Savon
miesten rohkea retki Viipuriin eivät jääneet seurauksia vaille:
Päättäväinen, pelvoton teko saa aina kannatusta! Sitä, joka ei auta
itseään, eivät auta muutkaan!
Ja Suomen kansa auttoi itse itseään! Siksi on se aina hädän tullen
saanut apua muodossa tai toisessa ja tulee aina saamaan!
1. Kansan nousu.

Monet syyt olivat vaikuttamassa Karjalan kansan nousuun, monet
tekijät yhdessä aiheuttivat jo heti alusta pitäen runsaan osanoton
vapaustaisteluun. Kuka lähti omasta alotteestaan puoltamaan lakia ja
oikeutta, henkeä ja kotinurkkia, kenellä kylä- tai pitäjäkunnat
pakoittavina määrääjinä selän takana seisoivat. Laajalle ulotettu
agitatsiooni oli omiaan vetämään välinpitämättömimmätkin mukaan.
Ne kylät ja kunnat, joissa ennen sotaa oli nuorisoseuroja,
voimistelu- ja urheiluseuroja, joissa nuorison valistamiseen oli aikaa
ja varoja uhrattu, ne kylät ja kunnat valveutuneimpina taisteluun
lähtivät. Niinpä Rautjärven pitäjästäkin lähti 326 miestä
vapaaehtoisesti vallananastajia ja verivihollisiamme ryssiä vastaan ja
Pyhäjärveltä 280 miestä. Edellinen on 6,2 % ja jälkimäinen 3,7 %
pitäjän koko väestöstä.
Mutta Rautjärvellä onkin nuorisoseura melkein joka kylässä!
Sitävastoin on Joutsenon pitäjässä vain muutamia nuorisoseuroja,
niinpä lähtikin sieltä kaiken kaikkiaan 83 vapaaehtoista eli 1,3 %
rintamalle siitä huolimatta, että taisteltiin aivan kotinurkista.
Myöskään ei meidän tule unhoittaa sitä vaikutusta, mikä on
paikkakunnan johtavilla henkilöillä ympäristöönsä: joko kaikki
yhdessä tai ei ollenkaan! Ja Rautjärvellä kokosi kapteeni Astola
miehet yhteistoimintaan! Samoin Joensuussa ylioppilas Paul Veikko
Raatikainen, joka kaatui Jänhiälän taistelussa huhtikuun 5 päivänä
Joutsenon rintamalla.
Olojen pakosta jakautui osanotto ja sotilasrasitus epätasaisesti eri
kunnille, mutta tietääkseni ei siitä yksikään kunta ole vielä valitusta
tehnyt. Kunnia-asiakseen sen ovat katsoneet ja kunniaksi se tulee
jäämäänkin!

Edelläolevassa en ole kosketellut tapahtumia Savonlinnan
ympäristössä, joka täydelleen lukeutui Karjalan taistelujen piiriin ja
josta monta reipasta komppaniaa saapui Vuoksen rintamalle. Älköön
käsitettäkö minua väärin, joskin tässä yhteydessä näin lyhyesti
julkituon vilpittömät kiitokseni ja rehellisen tunnustukseni niistä
ansiokkaista palveluksista, joita Savonlinnan ja sen ympäristön
väestö teki valkoiselle armeijalle Antrean rintamalla.
Tulkoon tässä yhteydessä myöskin mainituksi se, että marraskuun
"rankaisuretkikunnan" vaikutus oli aivan päinvastainen sille, mitä sillä
oli tarkoitettu. Kiivaimmat vastustajansa sai punakaarti sieltä, missä
mainittu retkikunta oli eniten rähjännyt. Ja niinpä oli se kaivanut
kuoppaa itselleen! Myöskin on täysi arvonsa annettava sille seikalle,
että ryssäviha on Karjalassa ollut jo ammoisista ajoista elävänä ja
että Venäjästä irti-pyrkimys on jo kauan ollut täysin selvänä
karjalaisten tajunnassa. Rinnastaen nämä seikat herkän karjalaisen
luonteen kanssa, onkin hyvin ymmärrettävää se, että karjalaiset,
tajuten Vuoksen rintaman tärkeyden jo varhain ryhtyivät miehissä
puolustamaan kotoisia seutuja ja maakuntansa pääkaupunkia.
Karjalan ja Savon miesten retki Viipuriin on tunnustettava
vapaustaisteluumme nähden paljon merkitseväksi teoksi, joskaan
sillä ei saavutettu sitä, mitä oli tarkoitettu. Jos tuo joukko, sen sijaan
että se nyt marssi suoraan suden suuhun ja oli pakoitettu heti
vetäytymään sieltä ulos, jos se olisi pysähtynyt Taliin ja sieltä
läsnäolollaan uhannut kaiken aikaa Viipurin rauhanhäiritsijöitä, —
kuten alkuperäinen suunnitelma kai lienee ollutkin, — niin olisi sen
vaikutus todennäköisesti ollut paljon suurempi niihin neuvotteluihin
nähden, joita käytiin hallituksen jäsenten ja punakaartilaisten
edustajien kanssa Viipurissa. Lausumalta jääköön myöskin arvelut
siitä, miten taistelujen vastaisen kehityksen olisi silloin käynyt, kun

olisivat asettuneet Talin vahvasti varustettuihin, venäläisten
puolustusasemiin ja kaikessa rauhassa muodostaneet
taistelurintaman Viipuria vastaan! Mutta kuten jo sanoin, tämä retki
on sittenkin ollut merkityksellinen, sillä se oli vapaustaistelumme
alkuna; siihen vedottiin Helsingissä ja muualla Suomessa, kun
koottiin lainkuuliaista väestöä estämään kapinahankkeita, ja siitä
saivat punakapinan johtajatkin ratkaisevan sysäyksen rikollisen
yrityksensä alkamiseen! Moraalisesti vaikutti se punaisiin yllättävästi,
valkoisiin aineksiin rohkaisevasti. Se järkytti jo alun pitäen ihmisten
sielunelämää ja — ennen kaikkea — herätti nukkuvankin
miehuudentunnon!
2. Tappioluettelo.
Vaikkakin taistelut olivat kiivaat ja vihollisella käytettävänään, voin
sanoa, rajaton määrä ampumatarpeita ja aseita, niin olivat
tappiomme verrattain vähäiset.
Taistelujen kahtena ensi viikkona oli kaatuneitten luku viikkoa
kohti kahdeksan ja haavoittuneiden edellistä viikkoa kohti 12 ja
jälkimäistä 8. Kolmannella taisteluviikolla jakautuivat tappiot
kummallisesti: kaatuneita oli 16 ja haavoittuneita vain 3. Neljännellä
viikolla oli kaatuneita 19 ja haavoittuneita 23.
Tähän asti olivat viikkotappiot, kuten näemme, uskomattomat
pienet, enkä ollenkaan ihmettele, jos pahat kielet ja ilkeämieliset
ihmiset käyttivät tilaisuutta hyväkseen parjaamalla Antrean
pääesikuntaa ja uskottelemalla herkkäuskoisille, että muka
kaatuneitten lukumäärä todellisuudessa oli paljoa suurempi ja että
ruumiit piiloitettiin suuriin varastohuoneihin. Tämänkaltaisia juoruja
levittivät punaiset ainekset koettaen saada kylvetyksi epäilystä ja

katkeruutta kansaan, mutta se oli turhaa. Taistelut toivat
ennenpitkää liiankin hyvin ilmi heidän puheittensa perättömyyden,
sillä jo viidennellä taisteluviikolla on kaatuneitten luku 32 ja
haavoittuneitten 46.
Kuudes viikko oli säästeliäämpi kaatuneihin mutta sitä anteliaampi
haavoittuneihin nähden: edellisiä oli 27, jälkimäisiä 105. Sitä
seuraavalla eli seitsemännellä viikolla oli huomattavissa joltinenkin
aleneminen, kaatuneita 23 ja haavoittuneita 81, mutta maaliskuun
puolivälistä eli jo kahdeksas viikko otti sen kaksin verroin takaisin:
kaatuneita 41 ja haavoittuneita 176.
Vaikeimpia viikkoja olivat maaliskuun viimeinen ja huhtikuun
ensimäinen eli sodan yhdeksäs ja kymmenes viikko. Edellinen vaati
uhreikseen 113 kaatunutta ja 369 haavoittunutta, jälkimäinen 130
kaatunutta ja 271 haavoittunutta.
Sitä menoa jos olisi kestänyt kauemmin, niin hukka olisi perinyt,
sillä täyte- ja lisä-miehistöä ei ehtinyt vastaavasti saapua rintamalle.
Mutta onneksi olikin jo seuraava eli yhdestoista viikko suopeampi,
vaatien vain 90 kaatunutta ja 264 haavoittunutta. Ja kaksi
seuraavaa, kahdestoista ja kolmastoista viikko vaativat yhteensä vain
92 kaatunutta sekä 410 haavoittunutta, niistä edellinen 60
kaatunutta ja 205 haavoittunutta ja jälkimäinen 32 kaatunutta ja 205
haavoittunutta. Neljästoista vajanainen viikko ehti sekin
tempaamaan 24 kaatunutta ja 64 haavoittunutta.
Näiden lisäksi tulee vielä 8 kaatunutta ja 182 haavoittunutta, joista
ei ole saatu selville kaatumis- eikä haavoittumis-aikaa eikä paikkaa.
Yhteensä oli kaatuneita 623 ja haavoittuneita 2121.

Kuten jo sanoin, olivat tappiot verrattain vähäiset; kuitenkin kylliksi
kalliit, muistaaksemme vastaisuudessa niiden arvon.
Moni kelpo nuorukainen uupui kesken elämäntyötään; moni keski-
ikäinen jätti perheensä holhojaa vaille! Mutta isänmaan
itsenäisyyden, lain ja oikeuden loukkaamattomuuden, uskon ja isien
perinnön puolesta ja eteen tehdyt uhraukset eivät koskaan ole liian
suuret, joskin ne saattavat usein tuntua raskailta ja katkerilta.
Taloudelliset tappiot, vaikka olivatkin suuret, eivät kuitenkaan
jättäneet sitä kaipausta ja surua, mikä edellämainittujen
vapaustaistelijain, sankarien, ennenaikaisesta poistumisesta oli
luonnollisena seurauksena.
3. Yhteenveto.
Tästä Suomen vapaus- ja kansalaissodasta v. 1918 kertovat
jälkeentulevat polvet vielä vuosisatainkin takaa ja historia on
langettava oman jäävittömän tuomionsa siitä. Mutta koskaan ei
voida kieltää Suomen kansan oikein ajattelevalta osalta sitä
tunnustusta, minkä se on kunnollaan ansainnut! Eikä koskaan tule
unhoittumaan Suomen valkoisen armeijan isänmaallinen työ eikä sen
esimerkiksi kelpaava kuntoisuus! Rinnan kulkivat siinä herra ja
talonpoika, rinnan harmaapäävanhukset nuorien koulupoikain kera!
Ja rohkeat, vaivojaan säästämättömät neitoset alttiisti apuaan
antoivat, milloin sairaanhoitajattarina tulilinjoilla, milloin taas
talouspuuhissa velvollisuutensa täyttivät! Ja kaikki nämä yhdessä
tekivät sen, että valkoinen armeija oli luja ja murtumaton!
"Alku on aina hankala", sanotaan ja niin se oli Suomen
vapaustaistelussakin. Mutta sitä mukaa kuin asiat kehittyivät ja

toiminta laajeni, sitä mukaa se myöskin varmistui ja järjestyi.
Voittamalla aikaa, voitti valkoinen armeija monta etua.
Punakapinoitsijoilla sensijaan kaikki pyrki menemään sekaisin, vaikka
heillä olikin suuri joukko venäläisiä upseereja johtajinaan. Vuoksen
rintamallakin todettiin parinkymmenen 42:nnen armeijakunnan
entisen upseerin, kenraali Jeremejeffin johdolla, työskennelleen
punaryssäin riveissä.
Mutta onni suosi Suomen kansaa monessa suhteessa! Niinpä
siinäkin, että taistelut saatiin taukoamaan aikaisin keväällä.
Tykistötuli, joka paksun lumen takia ei ollut läheskään niin
vaarallinen, kuin mitä se olisi saattanut olla sulalle maalle, ei ehtinyt
myöskään tuhoamaan viljapeltoja eikä heinäniittyjä. Toiselta puolen
oli, kuten jo olen ennemminkin maininnut, paksusta lumesta se etu,
että punaryssät olivat sidotut rautatielinjojen ja maanteiden varsiin.
Heillä ei ollut siinä määrin suksia käytettävinään kuin oli
vastapuolella, ja ryssäthän eivät sitä paitsi osanneet hiihtää. Näin oli
rohkeilla suksijoukoilla tilaisuus hätyyttää punaisia milloin tahansa.
Ja kun tähän rinnastaa vielä punaisten alhaisen mieskurin, joka
vahtipalveluksessa on erittäin tärkeä, niin ymmärtää hyvin sen
hermostuneisuuden, mikä vallitsi heidän joukoissaan.
Myöntää kyllä täytyy, että rohkeitakaan miehiä ei punaisilta
puuttunut, mutta massapsykologia vei nekin mukaansa.
Kun hyökkäyskäsky huhtikuun 2 päivänä annettiin, oli punaisten
rintama vahvimmillaan: Heinjoelta Saimaaseen asti puolusti sitä n.
7680 miestä, joilla oli käytettävänään 37 eri suuruista tykkiä ja
ainakin 44 kunnossa ja toiminnassa olevaa konekivääriä. Tämä
vihollinen oli tuhottava vahvoissa asemissaan n. 3178 miehellä, 472
alipäälliköllä ja 109 upseerilla, joilla oli käytettävinään 17 tykkiä

hyvin rajoitetuilla ammusmäärillä ja 38 kovasti kuluneella
konekiväärillä.
Mutta Karjalan rykmentit täyttivät tehtävänsä ja historian
kirjoittajat tulevat aikanaan antamaan arvostelunsa niiden
suorittamista sotilaallisista liikkeistä.
Loppusanat.
On usein ihmetelty taistelujen sitkeyttä Raudun aseman luona, on
kummastellen kyselty: miksi juuri Ahvola joutui kiivaimpien
taistelujen temmellyskentäksi ja miksi punaryssät juuri sitä tietä
tahtoivat tunkeutua Antreaan? Samoin on lausuttu mielipiteitä siitä,
että esim. Heinjoen kautta tehty hyökkäys olisi taannut punaryssille
varman etenemisen ja voiton.
Näihin kyselyihin ja arveluihin voidaan vastata monella eri tavalla.
Niinpä voidaan väittää yhtä jos toistakin, eikä niitä voida millään
kumota. Minun yksityinen mielipiteeni — kuten jo olen ennemminkin
maininnut — on se, että punaisten ja ryssien sodankäynti oli
enemmän psykologista kuin strategista: tehtiin mitä milloinkin
päähän pälkähti ja äänestettiin päälliköt kumoon, silloin kuin yleinen
mielipide — mukavuus — katsoi sen tarpeelliseksi!
Mitä tulee taisteluihin Raudun aseman luona, niin on niillä
luonnolliset selityksensä siinä, että aukeat viljelysmaat ympäröivät
hevosenkengän muotoisena kaarena Raudun asemaa ja tarjosivat
edullisen puolustuslinjan. Tätä käytti hyväkseen jo jääkärivänrikki

Läheniemi vähäisen puolustusjoukkonsa kanssa ja sittemmin
"kiviniemen pataljoonan" päällikkö jääkäriluutnantti Ekman.
Aivan samoin vaikuttivat Vehkeenniityt ja aukeat viljelysniityt
Hannilan ja Kavantsaaren välillä sen, että punaryssät mielellään
pyrkivät metsäisiä kukkuloita kohti Ahvolassa: "Vakavampi mainen
matka!
Lempo menköhön merelle, surma suurelle selälle!"
Jos vihollinen olisi tehnyt hyökkäyksensä sieltä tai täällä, kuten
esim. Heinjoelta, olisi sen yritys saattanut paremminkin onnistua,
mutta kuka voi sen taata! Muistaen Heinjoen vanhojen miesten
testamentinteot ennen tappeluun lähtöä, koulupoikien kiihkoisen
innostuksen, miesten ja naisten uhrautuvaisen ja rohkean toiminnan
kaikkialla, rintamalla ja sen välittömässä läheisyydessä, uskallan
omalta osaltani olla sitä mieltä, että punaryssien olisi ollut yhtä
vaikeaa tulla sieltä kuin täältä! Vaikeammaksi olisi niiden etenemisen
estäminen käynyt, jos helmikuun 11 päivänä olisi luovuttu Hannilan
asemasta ja parhaassa tapauksessa Antreastakin, tai jos eräistä,
minulle käsittämättömistä syistä, ei sittenkään olisi oikealla hetkellä
saatu valmiiksi harjoitettua ja varustettua 8:tta jääkäripataljoonaa
Sortavalasta Rautuun. Silloin olisi täytynyt vetää vasen siipi
Suvannon yli, kuten minulla jo oli lupakin. Mutta mitä vaikeuksia siitä
taas olisi johtunut puolustukseen ja aikanaan tapahtuvaan
Kannaksen puhdistukseen nähden, sen voivat arvioida vain ne, jotka
tuntevat paikallisia oloja Karjalan Kannaksella, tai voivat kartoista
perinpohjaisesti tutustua niihin.
Kylliksi kauan kesti odotusta näinkin, ennenkuin valkoisen armeijan
päävoimat joutuivat ratkaisevaan rynnistykseen Karjalassa. Jääköön
historioitsijain ratkaistavaksi, pakoittivatko täysin pätevät syyt

valloittamaan ensiksi Tampereen ja sitten vasta Viipurin, kuin myös
senkin, oliko tähdellistä ylläpitää matkustajaliikennettä samaan
aikaan kuin sotaväen kiireellisen siirron piti tapahtua Keskisuomesta
Karjalaan. Ottaen huomioon sen, että Tampere valloitettiin jo
huhtikuun 5 päivänä ja Viipurin valloitukseen voitiin ryhtyä vasta
kolmen viikon kuluttua, tuntui kriitillisissä oloissa odottavasta
sotaväensiirtely tarpeettoman pitkäveteiseltä.
Mutta kolme Karjalan rykmenttiä erikoispataljoonineen pystyivät
täyttämään ne tehtävät, jotka Suomen tasavallan sotajoukkojen
ylipäällikkö sähkösanomamääräyksellä oli antanut:
1) mihin hintaan hyvänsä suojella Savon rataa,
2) puolustaa Vuoksen rintamaa ja
3) — jos mahdollista — estää joukkojen siirtelyä Viipurin—Pietarin
radalla.
Kumma kyllä, saapui tähän viimeiseen tehtävään nähden kielteisiä
määräyksiä aivan viime viikkoina ennen Viipurin valtausta. Mutta
siihen lienevät olleet omat pätevät syynsä siihenkin. Sillä aikaa
ehtivät punaiset kuitenkin kuljettaa Venäjältä suunnattomia määriä
kaikellaista tappotavaraa, aseita ja ammuksia, jotka kyllä tuottivat
meille tuntuvaa vahinkoa, mutta lisäsivät myöskin sotasaaliimme
suuruutta!
Valkoisen armeijan taistelut Antrean rintamalla olivat osaltaan
vaikuttaneet siihen, että Suomen maa taas noudatti laillisen
hallituksensa antamia määräyksiä, että se oli päässyt irti
vuosisataisesta sortajastaan, Venäjästä, ja että yhteiskunnallinen
järjestys ja lainturva säilyi Suomen maassa. Näin oli Suomen

valkoisen armeijan aseellinen voima luonut uuden Suomen, vapaan
ja itsenäisen Suomen, jonka oikeuksien ja yhtenäisen eheyden
puolesta jokainen oikein ajatteleva kansalainen on valmis uhraamaan
kaikkensa, verensä ja henkensä!

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