Prior to eating breakfast, 25 participants were randomly assigned to eat a large meal, 25 to eat a small meal, and 25 to eat nothing. Immediately following the meal, all participants took a memory test. The means and estimated population variances for the three groups on the memory test were: Large: M = 2.1, S2 = 1.0; Small: M = 2.5, S2 = 1.2; Nothing: M = 2.9, S2 = 0.8. Using the .05 significance level, does amount of breakfast eaten affect memory?
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. Conduct a planned contrast for Large Meal versus Small Meal (using the .05 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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