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Table 6.5 Results of t-test scores of prisoner (SC & TX) and non-prisoner (SC & TX)
The analysis for this question can be done with a speciﬁc form of the t-statistic that
makes a very important assumption: the samples are paired or matched . Matched
samples simply imply that the sample data is collected from the same 36 obser-
vations, in our case the same SC prisoners. This form of sampling controls for
individual differences in the observations by focusing directly on the special training
as a level of treatment. It also can be thought of as a before-and-after analysis. For
our analysis, there are two levels of training—standard training and special (EB)
training. The tool in the Data Analysis menu to perform this type of analysis is
t-Test: Paired Two-Sample for Means .
Exhibit 6.5 shows the dialog box for matched samples. The data entry is identical
to that of the two-sample assuming unequal variances in Exhibit 6.4. Before we per-
form the analysis, it is worthwhile to consider the outcome. From the data samples
collected in Table 6.2, we can see that the average score difference between the two
treatments is about 2 points (79.08 before; 81.06 after). More importantly, if you
examine the ﬁnal two data columns in Table 6.2, it is clear that every observation
for the prisoners with only standard training is improved when special training is
applied. Thus, an informal analysis suggests that scores deﬁnitely have improved.
We would not be as secure in our analysis if we achieved the same sample mean
score improvement, but the individual matched scores were not consistently higher.