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Data Preparation 25/04/12 5:00 AM

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Data Preparation
Data Preparation involves checking or logging the data in; checking the data for
accuracy; entering the data into the computer; transforming the data; and developing
and documenting a database structure that integrates the various measures.

Logging the Data
In any research project you may have data coming from a number of different
sources at different times:

mail surveys returns
coded interview data
pretest or posttest data
observational data

In all but the simplest of studies, you need to set up a procedure for logging the
information and keeping track of it until you are ready to do a comprehensive data
analysis. Different researchers differ in how they prefer to keep track of incoming
data. In most cases, you will want to set up a database that enables you to assess at
any time what data is already in and what is still outstanding. You could do this with
any standard computerized database program (e.g., Microsoft Access, Claris
Filemaker), although this requires familiarity with such programs. or, you can
accomplish this using standard statistical programs (e.g., SPSS, SAS, Minitab,
Datadesk) and running simple descriptive analyses to get reports on data status. It is
also critical that the data analyst retain the original data records for a reasonable
period of time -- returned surveys, field notes, test protocols, and so on. Most
professional researchers will retain such records for at least 5-7 years. For important
or expensive studies, the original data might be stored in a data archive. The data
analyst should always be able to trace a result from a data analysis back to the original
forms on which the data was collected. A database for logging incoming data is a
critical component in good research record-keeping.

Checking the Data For Accuracy
As soon as data is received you should screen it for accuracy. In some circumstances
doing this right away will allow you to go back to the sample to clarify any problems
or errors. There are several questions you should ask as part of this initial data
screening:

Are the responses legible/readable?
Are all important questions answered?
Are the responses complete?
Is all relevant contextual information included (e.g., data, time, place,
researcher)?

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In most social research, quality of measurement is a major issue. Assuring that the
data collection process does not contribute inaccuracies will help assure the overall
quality of subsequent analyses.

Developing a Database Structure
The database structure is the manner in which you intend to store the data for the
study so that it can be accessed in subsequent data analyses. You might use the same
structure you used for logging in the data or, in large complex studies, you might
have one structure for logging data and another for storing it. As mentioned above,
there are generally two options for storing data on computer -- database programs
and statistical programs. Usually database programs are the more complex of the two
to learn and operate, but they allow the analyst greater flexibility in manipulating the
data.

In every research project, you should generate a printed codebook that describes the
data and indicates where and how it can be accessed. Minimally the codebook should
include the following items for each variable:

variable name
variable description
variable format (number, data, text)
instrument/method of collection
date collected
respondent or group
variable location (in database)
notes

The codebook is an indispensable tool for the analysis team. Together with the
database, it should provide comprehensive documentation that enables other
researchers who might subsequently want to analyze the data to do so without any
additional information.

Entering the Data into the Computer
There are a wide variety of ways to enter the data into the computer for analysis.
Probably the easiest is to just type the data in directly. In order to assure a high level
of data accuracy, the analyst should use a procedure called double entry. In this
procedure you enter the data once. Then, you use a special program that allows you
to enter the data a second time and checks each second entry against the first. If
there is a discrepancy, the program notifies the user and allows the user to determine
the correct entry. This double entry procedure significantly reduces entry errors.
However, these double entry programs are not widely available and require some
training. An alternative is to enter the data once and set up a procedure for checking
the data for accuracy. For instance, you might spot check records on a random basis.
Once the data have been entered, you will use various programs to summarize the
data that allow you to check that all the data are within acceptable limits and
boundaries. For instance, such summaries will enable you to easily spot whether
there are persons whose age is 601 or who have a 7 entered where you expect a 1-to-
5 response.


Data Transformations
Once the data have been entered it is almost always necessary to transform the raw
data into variables that are usable in the analyses. There are a wide variety of
transformations that you might perform. Some of the more common are:

missing values

Many analysis programs automatically treat blank values as missing. In
others, you need to designate specific values to represent missing values.
For instance, you might use a value of -99 to indicate that the item is
missing. You need to check the specific program you are using to
determine how to handle missing values.

item reversals

On scales and surveys, we sometimes use reversal items to help reduce
the possibility of a response set. When you analyze the data, you want
all scores for scale items to be in the same direction where high scores
mean the same thing and low scores mean the same thing. In these
cases, you have to reverse the ratings for some of the scale items. For
instance, let's say you had a five point response scale for a self esteem
measure where 1 meant strongly disagree and 5 meant strongly agree.
One item is "I generally feel good about myself." If the respondent
strongly agrees with this item they will put a 5 and this value would be
indicative of higher self esteem. Alternatively, consider an item like
"Sometimes I feel like I'm not worth much as a person." Here, if a
respondent strongly agrees by rating this a 5 it would indicate low self
esteem. To compare these two items, we would reverse the scores of
one of them (probably we'd reverse the latter item so that high values
will always indicate higher self esteem). We want a transformation
where if the original value was 1 it's changed to 5, 2 is changed to 4, 3
remains the same, 4 is changed to 2 and 5 is changed to 1. While you
could program these changes as separate statements in most program,
it's easier to do this with a simple formula like:

New Value = (High Value + 1) - Original Value

In our example, the High Value for the scale is 5, so to get the new
(transformed) scale value, we simply subtract each Original Value from
6 (i.e., 5 + 1).

scale totals

Once you've transformed any individual scale items you will often want
to add or average across individual items to get a total score for the
scale.

categories

For many variables you will want to collapse them into categories. For



instance, you may want to collapse income estimates (in dollar amounts)
into income ranges.

Copyright ©2006, William M.K. Trochim, All Rights Reserved
Purchase a printed copy of the Research Methods Knowledge Base
Last Revised: 10/20/2006


Descriptive Statistics 25/04/12 5:01 AM

Home » Analysis »

Descriptive Statistics
Descriptive statistics are used to describe the basic features of the data in a study.
They provide simple summaries about the sample and the measures. Together with
simple graphics analysis, they form the basis of virtually every quantitative analysis of
data.

Descriptive statistics are typically distinguished from inferential statistics. With
descriptive statistics you are simply describing what is or what the data shows. With
inferential statistics, you are trying to reach conclusions that extend beyond the
immediate data alone. For instance, we use inferential statistics to try to infer from
the sample data what the population might think. Or, we use inferential statistics to
make judgments of the probability that an observed difference between groups is a
dependable one or one that might have happened by chance in this study. Thus, we
use inferential statistics to make inferences from our data to more general conditions;
we use descriptive statistics simply to describe what's going on in our data.

Descriptive Statistics are used to present quantitative descriptions in a manageable
form. In a research study we may have lots of measures. Or we may measure a large
number of people on any measure. Descriptive statistics help us to simply large
amounts of data in a sensible way. Each descriptive statistic reduces lots of data into
a simpler summary. For instance, consider a simple number used to summarize how
well a batter is performing in baseball, the batting average. This single number is
simply the number of hits divided by the number of times at bat (reported to three
significant digits). A batter who is hitting .333 is getting a hit one time in every three
at bats. One batting .250 is hitting one time in four. The single number describes a
large number of discrete events. Or, consider the scourge of many students, the
Grade Point Average (GPA). This single number describes the general performance
of a student across a potentially wide range of course experiences.

Every time you try to describe a large set of observations with a single indicator you
run the risk of distorting the original data or losing important detail. The batting
average doesn't tell you whether the batter is hitting home runs or singles. It doesn't
tell whether she's been in a slump or on a streak. The GPA doesn't tell you whether
the student was in difficult courses or easy ones, or whether they were courses in
their major field or in other disciplines. Even given these limitations, descriptive
statistics provide a powerful summary that may enable comparisons across people or
other units.

Univariate Analysis
Univariate analysis involves the examination across cases of one variable at a time.
There are three major characteristics of a single variable that we tend to look at:

the distribution
the central tendency

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the dispersion

In most situations, we would describe all three of these characteristics for each of the
variables in our study.

The Distribution. The distribution is a summary of the frequency of individual
values or ranges of values for a variable. The simplest distribution would list every
value of a variable and the number of persons who had each value. For instance, a
typical way to describe the distribution of college students is by year in college, listing
the number or percent of students at each of the four years. Or, we describe gender
by listing the number or percent of males and females. In these cases, the variable
has few enough values that we can list each one and summarize how many sample
cases had the value. But what do we do for a variable like income or GPA? With
these variables there can be a large number of possible values, with relatively few
people having each one. In this case, we group the raw scores into categories
according to ranges of values. For instance, we might look at GPA according to the
letter grade ranges. Or, we might group income into four or five ranges of income
values.

Table 1. Frequency distribution table.

One of the most common ways to describe a single variable is with a frequency
distribution Depending on the particular variable, all of the data values may be
distribution.
represented, or you may group the values into categories first (e.g., with age, price, or
temperature variables, it would usually not be sensible to determine the frequencies
for each value. Rather, the value are grouped into ranges and the frequencies
determined.). Frequency distributions can be depicted in two ways, as a table or as a
graph. Table 1 shows an age frequency distribution with five categories of age ranges
defined. The same frequency distribution can be depicted in a graph as shown in
Figure 2. This type of graph is often referred to as a histogram or bar chart.



Table 2. Frequency distribution bar chart.

Distributions may also be displayed using percentages. For example, you could use
percentages to describe the:

percentage of people in different income levels
percentage of people in different age ranges
percentage of people in different ranges of standardized test scores

Central Tendency. The central tendency of a distribution is an estimate of the
"center" of a distribution of values. There are three major types of estimates of
central tendency:

Mean
Median
Mode

The Mean or average is probably the most commonly used method of describing
central tendency. To compute the mean all you do is add up all the values and divide
by the number of values. For example, the mean or average quiz score is determined
by summing all the scores and dividing by the number of students taking the exam.
For example, consider the test score values:

15, 20, 21, 20, 36, 15, 25, 15

The sum of these 8 values is 167, so the mean is 167/8 = 20.875.

The Median is the score found at the exact middle of the set of values. One way to
compute the median is to list all scores in numerical order, and then locate the score
in the center of the sample. For example, if there are 500 scores in the list, score
#250 would be the median. If we order the 8 scores shown above, we would get:

15,15,15,20,20,21,25,36

There are 8 scores and score #4 and #5 represent the halfway point. Since both of
these scores are 20, the median is 20. If the two middle scores had different values,



you would have to interpolate to determine the median.

The mode is the most frequently occurring value in the set of scores. To determine
the mode, you might again order the scores as shown above, and then count each
one. The most frequently occurring value is the mode. In our example, the value 15
occurs three times and is the model. In some distributions there is more than one
modal value. For instance, in a bimodal distribution there are two values that occur
most frequently.

Notice that for the same set of 8 scores we got three different values -- 20.875, 20,
and 15 -- for the mean, median and mode respectively. If the distribution is truly
normal (i.e., bell-shaped), the mean, median and mode are all equal to each other.

Dispersion. Dispersion refers to the spread of the values around the central
tendency. There are two common measures of dispersion, the range and the standard
deviation. The range is simply the highest value minus the lowest value. In our
example distribution, the high value is 36 and the low is 15, so the range is 36 - 15 =
21.

The Standard Deviation is a more accurate and detailed estimate of dispersion
because an outlier can greatly exaggerate the range (as was true in this example where
the single outlier value of 36 stands apart from the rest of the values. The Standard
Deviation shows the relation that set of scores has to the mean of the sample. Again
lets take the set of scores:

15,20,21,20,36,15,25,15

to compute the standard deviation, we first find the distance between each value and
the mean. We know from above that the mean is 20.875. So, the differences from
the mean are:

15 - 20.875 = -5.875
20 - 20.875 = -0.875
21 - 20.875 = +0.125
20 - 20.875 = -0.875
36 - 20.875 = 15.125
15 - 20.875 = -5.875
25 - 20.875 = +4.125
15 - 20.875 = -5.875

Notice that values that are below the mean have negative discrepancies and values
above it have positive ones. Next, we square each discrepancy:

-5.875 * -5.875 = 34.515625
-0.875 * -0.875 = 0.765625
+0.125 * +0.125 = 0.015625
-0.875 * -0.875 = 0.765625
15.125 * 15.125 = 228.765625
-5.875 * -5.875 = 34.515625
+4.125 * +4.125 = 17.015625
-5.875 * -5.875 = 34.515625



Now, we take these "squares" and sum them to get the Sum of Squares (SS) value.
Here, the sum is 350.875. Next, we divide this sum by the number of scores minus 1.
Here, the result is 350.875 / 7 = 50.125. This value is known as the variance. To get
the standard deviation, we take the square root of the variance (remember that we
squared the deviations earlier). This would be SQRT(50.125) = 7.079901129253.

Although this computation may seem convoluted, it's actually quite simple. To see
this, consider the formula for the standard deviation:

In the top part of the ratio, the numerator, we see that each score has the the mean
subtracted from it, the difference is squared, and the squares are summed. In the
bottom part, we take the number of scores minus 1. The ratio is the variance and the
square root is the standard deviation. In English, we can describe the standard
deviation as:

the square root of the sum of the squared deviations from the mean divided
by the number of scores minus one

Although we can calculate these univariate statistics by hand, it gets quite tedious
when you have more than a few values and variables. Every statistics program is
capable of calculating them easily for you. For instance, I put the eight scores into
SPSS and got the following table as a result:

N 8
Mean 20.8750
Median 20.0000
Mode 15.00
Std. Deviation 7.0799
Variance 50.1250
Range 21.00



which confirms the calculations I did by hand above.

The standard deviation allows us to reach some conclusions about specific scores in
our distribution. Assuming that the distribution of scores is normal or bell-shaped
(or close to it!), the following conclusions can be reached:

approximately 68% of the scores in the sample fall within one standard
deviation of the mean
approximately 95% of the scores in the sample fall within two standard
deviations of the mean
approximately 99% of the scores in the sample fall within three standard
deviations of the mean

For instance, since the mean in our example is 20.875 and the standard deviation is
7.0799, we can from the above statement estimate that approximately 95% of the
scores will fall in the range of 20.875-(2*7.0799) to 20.875+(2*7.0799) or between
6.7152 and 35.0348. This kind of information is a critical stepping stone to enabling
us to compare the performance of an individual on one variable with their
performance on another, even when the variables are measured on entirely different
scales.



Correlation 25/04/12 5:02 AM

Home » Analysis » Descriptive Statistics »

Correlation
The correlation is one of the most common and most useful statistics. A correlation
is a single number that describes the degree of relationship between two variables.
Let's work through an example to show you how this statistic is computed.

Correlation Example
Let's assume that we want to look at the relationship between two variables, height
(in inches) and self esteem. Perhaps we have a hypothesis that how tall you are
effects your self esteem (incidentally, I don't think we have to worry about the
direction of causality here -- it's not likely that self esteem causes your height!). Let's
say we collect some information on twenty individuals (all male -- we know that the
average height differs for males and females so, to keep this example simple we'll just
use males). Height is measured in inches. Self esteem is measured based on the
average of 10 1-to-5 rating items (where higher scores mean higher self esteem).
Here's the data for the 20 cases (don't take this too seriously -- I made this data up to
illustrate what a correlation is):

Person Height Self Esteem
1 68 4.1
2 71 4.6
3 62 3.8
4 75 4.4
5 58 3.2
6 60 3.1
7 67 3.8
8 68 4.1
9 71 4.3
10 69 3.7
11 68 3.5
12 67 3.2
13 63 3.7
14 62 3.3
15 60 3.4
16 63 4.0
17 65 4.1
18 67 3.8
19 63 3.4
20 61 3.6

Now, let's take a quick look at the histogram for each variable:

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And, here are the descriptive statistics:

Variable Mean StDev Variance Sum Minimum Maximum Range
Height 65.4 4.40574 19.4105 1308 58 75 17
Self
3.755 0.426090 0.181553 75.1 3.1 4.6 1.5
Esteem

Finally, we'll look at the simple bivariate (i.e., two-variable) plot:

You should immediately see in the bivariate plot that the relationship between the
variables is a positive one (if you can't see that, review the section on types of
relationships) because if you were to fit a single straight line through the dots it
would have a positive slope or move up from left to right. Since the correlation is
nothing more than a quantitative estimate of the relationship, we would expect a
positive correlation.

What does a "positive relationship" mean in this context? It means that, in general,
higher scores on one variable tend to be paired with higher scores on the other and
that lower scores on one variable tend to be paired with lower scores on the other.
You should confirm visually that this is generally true in the plot above.

Calculating the Correlation
Now we're ready to compute the correlation value. The formula for the correlation
is:



We use the symbol r to stand for the correlation. Through the magic of mathematics
it turns out that r will always be between -1.0 and +1.0. if the correlation is negative,
we have a negative relationship; if it's positive, the relationship is positive. You don't
need to know how we came up with this formula unless you want to be a statistician.
But you probably will need to know how the formula relates to real data -- how you
can use the formula to compute the correlation. Let's look at the data we need for
the formula. Here's the original data with the other necessary columns:

Self Esteem
Person Height (x) x*y x*x y*y
(y)
1 68 4.1 278.8 4624 16.81
2 71 4.6 326.6 5041 21.16
3 62 3.8 235.6 3844 14.44
4 75 4.4 330 5625 19.36
5 58 3.2 185.6 3364 10.24
6 60 3.1 186 3600 9.61
7 67 3.8 254.6 4489 14.44
8 68 4.1 278.8 4624 16.81
9 71 4.3 305.3 5041 18.49
10 69 3.7 255.3 4761 13.69
11 68 3.5 238 4624 12.25
12 67 3.2 214.4 4489 10.24
13 63 3.7 233.1 3969 13.69
14 62 3.3 204.6 3844 10.89
15 60 3.4 204 3600 11.56
16 63 4 252 3969 16
17 65 4.1 266.5 4225 16.81
18 67 3.8 254.6 4489 14.44
19 63 3.4 214.2 3969 11.56
20 61 3.6 219.6 3721 12.96
Sum = 1308 75.1 4937.6 85912 285.45

The first three columns are the same as in the table above. The next three columns
are simple computations based on the height and self esteem data. The bottom row
consists of the sum of each column. This is all the information we need to compute
the correlation. Here are the values from the bottom row of the table (where N is 20
people) as they are related to the symbols in the formula:

Now, when we plug these values into the formula given above, we get the following
(I show it here tediously, one step at a time):



So, the correlation for our twenty cases is .73, which is a fairly strong positive
relationship. I guess there is a relationship between height and self esteem, at least in
this made up data!

Testing the Significance of a Correlation
Once you've computed a correlation, you can determine the probability that the
observed correlation occurred by chance. That is, you can conduct a significance test.
Most often you are interested in determining the probability that the correlation is a
real one and not a chance occurrence. In this case, you are testing the mutually
exclusive hypotheses:

Null Hypothesis: r=0
Alternative Hypothesis: r <> 0

The easiest way to test this hypothesis is to find a statistics book that has a table of
critical values of r. Most introductory statistics texts would have a table like this. As
in all hypothesis testing, you need to first determine the significance level. Here, I'll
use the common significance level of alpha = .05. This means that I am conducting a
test where the odds that the correlation is a chance occurrence is no more than 5 out
of 100. Before I look up the critical value in a table I also have to compute the
degrees of freedom or df. The df is simply equal to N-2 or, in this example, is 20-2 =
18. Finally, I have to decide whether I am doing a one-tailed or two-tailed test. In
this example, since I have no strong prior theory to suggest whether the relationship
between height and self esteem would be positive or negative, I'll opt for the two-
tailed test. With these three pieces of information -- the significance level (alpha =
.05)), degrees of freedom (df = 18), and type of test (two-tailed) -- I can now test the
significance of the correlation I found. When I look up this value in the handy little
table at the back of my statistics book I find that the critical value is .4438. This
means that if my correlation is greater than .4438 or less than -.4438 (remember, this
is a two-tailed test) I can conclude that the odds are less than 5 out of 100 that this is
a chance occurrence. Since my correlation 0f .73 is actually quite a bit higher, I
conclude that it is not a chance finding and that the correlation is "statistically
significant" (given the parameters of the test). I can reject the null hypothesis and
accept the alternative.

The Correlation Matrix
All I've shown you so far is how to compute a correlation between two variables. In



most studies we have considerably more than two variables. Let's say we have a study
with 10 interval-level variables and we want to estimate the relationships among all
of them (i.e., between all possible pairs of variables). In this instance, we have 45
unique correlations to estimate (more later on how I knew that!). We could do the
above computations 45 times to obtain the correlations. Or we could use just about
any statistics program to automatically compute all 45 with a simple click of the
mouse.

I used a simple statistics program to generate random data for 10 variables with 20
cases (i.e., persons) for each variable. Then, I told the program to compute the
correlations among these variables. Here's the result:

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10
C1 1.000
C2 0.274 1.000
C3 -0.134 -0.269 1.000
C4 0.201 -0.153 0.075 1.000
C5 -0.129 -0.166 0.278 -0.011 1.000
C6 -0.095 0.280 -0.348 -0.378 -0.009 1.000
C7 0.171 -0.122 0.288 0.086 0.193 0.002 1.000
C8 0.219 0.242 -0.380 -0.227 -0.551 0.324 -0.082 1.000
C9 0.518 0.238 0.002 0.082 -0.015 0.304 0.347 -0.013 1.000
C10 0.299 0.568 0.165 -0.122 -0.106 -0.169 0.243 0.014 0.352 1.000

This type of table is called a correlation matrix. It lists the variable names (C1-C10)
down the first column and across the first row. The diagonal of a correlation matrix
(i.e., the numbers that go from the upper left corner to the lower right) always
consists of ones. That's because these are the correlations between each variable and
itself (and a variable is always perfectly correlated with itself). This statistical program
only shows the lower triangle of the correlation matrix. In every correlation matrix
there are two triangles that are the values below and to the left of the diagonal (lower
triangle) and above and to the right of the diagonal (upper triangle). There is no
reason to print both triangles because the two triangles of a correlation matrix are
always mirror images of each other (the correlation of variable x with variable y is
always equal to the correlation of variable y with variable x). When a matrix has this
mirror-image quality above and below the diagonal we refer to it as a symmetric matrix.
A correlation matrix is always a symmetric matrix.

To locate the correlation for any pair of variables, find the value in the table for the
row and column intersection for those two variables. For instance, to find the
correlation between variables C5 and C2, I look for where row C2 and column C5 is
(in this case it's blank because it falls in the upper triangle area) and where row C5
and column C2 is and, in the second case, I find that the correlation is -.166.

OK, so how did I know that there are 45 unique correlations when we have 10
variables? There's a handy simple little formula that tells how many pairs (e.g.,
correlations) there are for any number of variables:

where N is the number of variables. In the example, I had 10 variables, so I know I
have (10 * 9)/2 = 90/2 = 45 pairs.

Other Correlations
The specific type of correlation I've illustrated here is known as the Pearson Product
Moment Correlation. It is appropriate when both variables are measured at an
interval level. However there are a wide variety of other types of correlations for
other circumstances. for instance, if you have two ordinal variables, you could use
the Spearman rank Order Correlation (rho) or the Kendall rank order Correlation
(tau). When one measure is a continuous interval level one and the other is
dichotomous (i.e., two-category) you can use the Point-Biserial Correlation. For
other situations, consulting the web-based statistics selection program, Selecting
Statistics at http://trochim.human.cornell.edu/selstat/ssstart.htm.



Inferential Statistics 25/04/12 5:02 AM

Home » Analysis »

Inferential Statistics
With inferential statistics, you are trying to reach conclusions that extend beyond the
immediate data alone. For instance, we use inferential statistics to try to infer from
the sample data what the population might think. Or, we use inferential statistics to
make judgments of the probability that an observed difference between groups is a
dependable one or one that might have happened by chance in this study. Thus, we
use inferential statistics to make inferences from our data to more general conditions;
we use descriptive statistics simply to describe what's going on in our data.

Here, I concentrate on inferential statistics that are useful in experimental and quasi-
experimental research design or in program outcome evaluation. Perhaps one of the
simplest inferential test is used when you want to compare the average performance
of two groups on a single measure to see if there is a difference. You might want to
know whether eighth-grade boys and girls differ in math test scores or whether a
program group differs on the outcome measure from a control group. Whenever you
wish to compare the average performance between two groups you should consider
the t-test for differences between groups.

Most of the major inferential statistics come from a general family of statistical
models known as the General Linear Model. This includes the t-test, Analysis of
Variance (ANOVA), Analysis of Covariance (ANCOVA), regression analysis, and
many of the multivariate methods like factor analysis, multidimensional scaling,
cluster analysis, discriminant function analysis, and so on. Given the importance of
the General Linear Model, it's a good idea for any serious social researcher to
become familiar with its workings. The discussion of the General Linear Model here
is very elementary and only considers the simplest straight-line model. However, it
will get you familiar with the idea of the linear model and help prepare you for the
more complex analyses described below.

One of the keys to understanding how groups are compared is embodied in the
notion of the "dummy" variable. The name doesn't suggest that we are using
variables that aren't very smart or, even worse, that the analyst who uses them is a
"dummy"! Perhaps these variables would be better described as "proxy" variables.
Essentially a dummy variable is one that uses discrete numbers, usually 0 and 1, to
represent different groups in your study. Dummy variables are a simple idea that
enable some pretty complicated things to happen. For instance, by including a simple
dummy variable in an model, I can model two separate lines (one for each treatment
group) with a single equation. To see how this works, check out the discussion on
dummy variables.

One of the most important analyses in program outcome evaluations involves
comparing the program and non-program group on the outcome variable or
variables. How we do this depends on the research design we use. research designs
are divided into two major types of designs: experimental and quasi-experimental.
Because the analyses differ for each, they are presented separately.

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Inferential Statistics 25/04/12 5:02 AM

Experimental Analysis. The simple two-group posttest-only randomized
experiment is usually analyzed with the simple t-test or one-way ANOVA. The
factorial experimental designs are usually analyzed with the Analysis of Variance
(ANOVA) Model. Randomized Block Designs use a special form of ANOVA
blocking model that uses dummy-coded variables to represent the blocks. The
Analysis of Covariance Experimental Design uses, not surprisingly, the Analysis of
Covariance statistical model.

Quasi-Experimental Analysis. The quasi-experimental designs differ from the
experimental ones in that they don't use random assignment to assign units (e.g.,
people) to program groups. The lack of random assignment in these designs tends to
complicate their analysis considerably. For example, to analyze the Nonequivalent
Groups Design (NEGD) we have to adjust the pretest scores for measurement error
in what is often called a Reliability-Corrected Analysis of Covariance model. In the
Regression-Discontinuity Design, we need to be especially concerned about
curvilinearity and model misspecification. Consequently, we tend to use a
conservative analysis approach that is based on polynomial regression that starts by
overfitting the likely true function and then reducing the model based on the results.
The Regression Point Displacement Design has only a single treated unit.
Nevertheless, the analysis of the RPD design is based directly on the traditional
ANCOVA model.

When you've investigated these various analytic models, you'll see that they all come
from the same family -- the General Linear Model. An understanding of that model
will go a long way to introducing you to the intricacies of data analysis in applied and
social research contexts.


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