3. Consider the functions { 1 2} and {()11 ()21 ()12 + ()22} under the two-way complete model (6.2.2). (a) Verify

3. Consider the functions {α∗ 1 − α∗ 2} and {(αβ)11 − (αβ)21 − (αβ)12 + (αβ)22} under the two-way complete model (6.2.2).

(a) Verify that the functions are estimable contrasts.

(b) Discuss the meaning of each of these contrasts for plot

(d) of Fig. 6.1, p. 140, and for plot (g) of Fig. 6.2, p. 141.

(c) If a = b = 3, give the list of contrast coefficients for each contrast, first for the parameters involved in the contrast, and then in terms of the parameters τij of the equivalent cell-means model.