5. A set of hypothetical data is given in Table 14.18 for a partially confounded 32 experiment in 6 blocks of 3. The design is made up of two single-replicate designs: The first confounds the contrasts (AB; A2 B2) from the interaction, while the second confounds the contrasts (AB2; A2 B).

(a) By hand, write out the estimates of the linear and quadratic contrasts for the main effects and their associated variances.

(b) Using the contrast estimates in part (a), calculate the sums of squares for A and B.

(c) Calculate the least squares estimates of a pair of orthogonal contrasts for (AB2; A2 B) from the first replicate and the estimates of a pair of orthogonal contrasts for (AB; A2 B2) from the second replicate. Using these contrast estimates, calculate the sum of squares for the AB interaction (adjusted for blocks).

(d) Prepare an analysis of variance table. Test any hypotheses that you think are of interest and state your conclusions about the two factors and their interaction.

(e) Check your analysis in part

(d) using a computer program.