To study the effectiveness of possible treatments for insomnia, a sleep researcher conducted a study in which four participants were instructed to count sheep (the Sheep Condition), four were told to concentrate on their breathing (the Breathing Condition), and four were not given any special instructions (the Control Condition). The average number of minutes taken for participants to fall asleep over the next seven days were 39, 33, 42, and 38 minutes for the Sheep condition; 33, 25, 31, and 27 minutes for the Breathing condition; and 44, 41, 38, and 41 for the Control condition. Using the .01 significance level, did the different techniques have different effects?
a. Use the five steps of hypothesis testing.
b. Sketch the distributions involved.
c. Figure the effect size of this study and indicate whether it is nearer to small, medium, or large.
d. Figure a planned contrast between the means for those in the Sheep Condition versus those in the Breathing Condition using the .05 significance level.
e. Conduct Scheffé's test for the groups in (d) and indicate the F cutoff, the F you would use for the comparison, and the hypothesis-testing decision (reject or do not reject).
f. Explain the logic of what you did to a person who is familiar with the t test for independent means, but who knows nothing about the analysis of variance. (Be sure your explanation includes the logic of comparing within-groups to between-groups population variance estimates, the logic of how each of these is figured, the F distribution, and the F table.)
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