Many studies have found a negative correlation between amount of exercise and level of depression. People who exercise tend to be less depressed than people who do not exercise. Recall from Chapter 7, however, that correlation does not prove causation. (Does exercising regularly lower depression, or are less depressed individuals more likely to exercise?) Suppose we wished to investigate the effects of exercise on depression. We randomly assign 20 subjects, who tests show suffer from depression, to one of two groups of 10: those who will participate in an aerobic exercise program 4 days a week for 2 months, and those who are not prescribed an exercise program. A study similar to this was, in fact, conducted by McCann and Holmes (1984). Let us assume that one of the subjects in the exercise group and two of those in the control group drop out before completing the study. At the end of the study, the hypothetical depression scores for the remaining subjects are as follows (higher scores indicate higher levels of depression):
(a) State formally the hypotheses necessary to conduct a non directional test of no difference between the two population means.
(b) Complete the test at the .05 level of significance, and state your conclusion.
(c) Does it matter which group we designate as X and which as Y?
(d) Compute the estimated effect size, g, and r.