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Exhibit 6.4 Data analysis tool for t-test unequal variances
6.5.5 Do Prisoners Score Higher Than Non-Prisoners Regardless
of the State?
Earlier we suggested that the analysis did not consider state afﬁliation, but in fact
our selection of data has explicitly done so—only Texas data was used. The data is
controlled for the state afﬁliation variable; that is, the state variable is held constant
since all observations are from Texas. What might be a more appropriate analysis if
we do not want to hold the state variable constant and thereby make a statement that
is not state dependent? The answer is relatively simple: combine the SC and Texas
non-prisoner scores in Exhibit 6.2 columns C and E (72 observations; 36 + 36) and
the SC and Texas Prisoner scores in column D and F (also 72). Note that we use
Column F data rather than G since we are interested in the standard training only.
Now we are ready to perform the analysis on these larger sample data sets, and
fortuitously, more data is more reliable. The outcome is now independent of the
state afﬁliation of the observations. In Table 6.5 we see that the results are similar
to those in Table 6.4: we reject the null hypothesis in favor of the alternative that
there is a difference. A t-statistic of approximately – 3.085 (cell F11) and a p-value
of 0.0025 (cell F14) is evidence of the need to reject the null hypothesis; – 3.085 is
less than the critical value –1.977 (cell D21) and 0.0025 is less than
α
(0.05).
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