Exam 12: Multiple Comparison Procedures

A one-factor fixed-effects ANOVA is performed on data for 5 groups of unequal sizes, and H₀ is rejected at the .05 level of significance. Using the Scheffe' procedure, test the contrast that $\bar{Y}_{.1}-\frac{P_{s 2}+P_{s 3}}{2}$ at the .05 level of significance given the following information: df_with = 30, $\bar{Y}_{.1}$ = 5, n₁ = 6, $\bar{Y}_{.2}$ = 7.5, n₂ = 6, $\bar{Y}_{.3}$ = 8.5, n₃ = 6, and MS_with = 9.

In the same study described in item 16, if the researcher is now interested in comparing the scores of the class taught by the traditional method against the average of the classes taught by all the alternative methods, which procedure should she use?

Consider the situation where there are J = 3 groups of subjects. Answer the following questions: a. Construct a set of orthogonal contrasts and show that they are orthogonal. b. Construct a set of contrasts for Dunnett's test (use group 1 as the reference group). Are these contrasts orthogonal? Why? c. Construct a set of contrasts for pairwise comparisons. Are these contrasts orthogonal? Why?

In an experiment, $\bar{Y}_{1}$ =10, $\bar{Y}_{2}$ =20, and $\bar{Y}_{3}$ =40. Tukey HSD shows that $\mu$ ₂- $\mu$ ₁ is a significant contrast. What will you find out about $\mu$ ₃- $\mu$ ₁ and $\mu$ ₃- $\mu$ ₂ if the same procedure and same $\alpha$ level are used?

Which of the following statements about post hoc tests is true?

A researcher used Fisher's LSD to test three contrasts: $\mu$ ₁- $\mu$ ₂, $\mu$ ₁- $\mu$ ₃, $\mu$ ₁-( $\mu$ ₂+ $\mu$ ₃)/2. Evaluate this practice.

For pairwise post hoc contrasts with unequal group variances, which of the following MCPs is most appropriate?

A one-factor fixed-effects ANOVA is performed on data from three groups of equal size (n = 15) and equal variances, and H₀ is rejected at the .05 level. The following values were computed: MS_with = 60 and the sample means are $\bar{Y}_{.1}$ = 25, $\bar{Y}_{.2}$ = 20, and $\bar{Y}_{.3}$ = 12. Use the Tukey HSD method to test all possible pairwise contrasts ( $\alpha$ = .05).

Following a significant omnibus ANOVA F test, Scheffe; MCP is conducted. Which of the following results is never possible?

If J = 4, which of the following statements is true?