(Equations 8.6 (page 167) show how the parameters in a dummy-coded twoway ANOVA model can be expressed in terms of the cell means jk when

(Equations 8.6 (page 167) show how the parameters in a dummy-coded twoway ANOVA model can be expressed in terms of the cell means µjk when the number of levels of the row factor R is r ¼ 2 and the number of levels of the column factor C is c ¼ 3.

(a) Explain why the hypotheses H0: β1 ¼ 0 and H0: γ1 ¼ γ2 ¼ 0 cannot reasonably be construed as tests of the R and C main effects when the interaction parameters δ11 and

δ12 are nonzero.

(b) Now suppose that δ11 and δ12 are zero but that we fit the full model in Equation 8.5 to the data. Explain why H0: β1 ¼ 0 and H0: γ1 ¼ γ2 ¼ 0 now test hypotheses about the R and C main effects but do so in a nonoptimal manner (i.e., with low power)