In an experiment described in Kirk (1982), four methods for teaching arithmetic were being evaluated. Thirty-two students were randomly assigned to four classrooms, each with eight students. An intelligence test was administered to each student at the beginning of the experiment.

The resulting scores (x) are used to adjust the arithmetic achievement scores (y) obtained at the conclusion of the experiment for differences in intelligence among the students. The results are recorded as follows:

Method 1 Method 2 Method 3 Method 4 y xy xy x y x 3 42 4 47 7 61 7 65 6 57 5 49 8 65 8 74 3 33 4 42 7 64 9 80 3 47 3 41 6 56 8 73 1 32 2 38 5 52 10 85 2 35 3 43 6 58 10 82 2 33 4 48 5 53 9 78 2 39 3 45 6 54 11 89

a. Use proc glm and the one-way covariance (equal slopes)

model to analyze this data. Construct an adjusted ANOVA table.

b. Using the above ANOVA table, test the hypothesis of H0 : μ1 =

μ2 = μ3 = μ4 (use the p-value and state decision).

c. Construct 95% confidence intervals for all differences in pairs of means (e.g., μa − μb) adjusted for multiple testing using the Tukey method.

d. What does the test of H0 : β = 0 tell you? Test this hypothesis using the above adjusted ANOVA table and state your conclusion.

e. Construct an analysis of variance that is not adjusted for the intelligence score. What conclusion can you draw from this ANOVA table.