Exercises 217more aroused. This is what Jones and Tukey call a “reversal,” and the probability of making
this error if we use a one-tailedtest at a 5 .05 is .05. Alternatively it could be that mH.mN
but that we make the error of concluding that the nonhomophobic participants are less
aroused. Again with a one-tailed test the probability of making this error is .05. It is not
possible for us to make both of these errors because one of the hypotheses is true, so using
a one-tailedtest (in both directions) at a5.05 gives us a 5% error rate. In our particular
example the critical value for a one-tailed test on 62 dfis approximately 1.68. Because our
obtained value of twas 2.48, we will conclude that homophobic participants are more
aroused, on average, than nonhomophobic participants. Notice that in writing this para-
graph I have not used the phrase “Type I error,” because that refers to rejecting a true null,
and I have already said that the null can’t possibly be true. In fact, notice that my conclu-
sion did not contain the phrase “rejecting the hypothesis.” Instead I referred to “drawing a
conclusion.” These are subtle differences, but I hope this example clarifies the position
taken by Jones and Tukey.Key Terms
Sampling distribution of the mean (7.1)
Central limit theorem (7.1)
Uniform (rectangular) distribution (7.1)
Standard error (7.2)
Student’s tdistribution (7.3)
Point estimate (7.3)
Confidence limits (7.3)
Confidence interval (7.3)
plevel (7.3)
Matched samples (7.4)
Repeated measures (7.4)
Related samples (7.4)
Matched-sample ttest (7.4)
Difference scores (7.4)
Gain scores (7.4)
Cohen’s d(7.4)
Sampling distribution of differences
between means (7.5)
Variance sum law (7.5)
Standard error of differences
between means (7.5)
Weighted average (7.5)Pooled variance estimate (7.5)
Homogeneity of variance (7.7)
Heterogeneous variances (7.7)
Behrens–Fisher problem (7.7)
Welch–Satterthwaite solution (7.7)
Robust (7.7)Exercises
7.1 The following numbers represent 100 random numbers drawn from a rectangular popula-
tion with a mean of 4.5 and a standard deviation of .2.7. Plot the distribution of these digits.
648787082857
482690264904
934282041474
174241428797
374731671872
762186233654
172102608324
384570842863
7351