. Which approach is preferable, if homogeneity holds?

A psychologist designs a study with four independent groups. However, the number of subjects in each group is very unequal: HI = 10, n2 = 50, n3 = 50, and n4 = 10. One specific comparison of interest is the contrast of Groups 1 and 4. Believing that homogeneity of variance holds here, he decides to use MSw as the error term for his comparison. However, his research assistant argues that even with homogeneity, the data in Groups 2 and 3 should be completely ignored because Groups 1 and 4 are so much smaller. In other words, the research assistant maintains that the large samples for Groups 2 and 3 make the observed F for comparing Groups 1 and 4 much larger than it would be if a separate error term were used (i.e., an error term based just on Groups 1 and 4). Thus, even with homogeneity, the test should be based only on the 10 subjects in Group 1 and 10 subjects in Group 4 to avoid an inflated F from the large sample in Groups 2 and 3. a. Would you expect the observed F to be larger using MSW instead of a separate error term, if homogeneity holds? Why or why not? b. How does the critical F based on AfSw compare to the critical F based on a separate error term? c. Which approach is preferable, if homogeneity holds?


 

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