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 µ jk when the number of levels of the row factor R is r = 2 and the...

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 µ_jk
when the number of levels of the row factor R is r = 2 and the number of levels of the column factor C is c = 3.

(a) Explain why the hypotheses H₀: β₁
= 0 and H₀: γ₁
= γ₂
= 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
= 0 and H₀: γ₁
= γ₂
= 0 now test hypotheses about the R and C main effects but do so in a nonoptimal manner (i.e., with low power).