Box, Hunter, and Hunter (1978) describe a two-factor experiment in which all combinations of three poisons (factor A) and four antidotes (factor B) are considered. Four replicates (laboratory animals) are randomly allocated to each treatment combination. The survival times are shown in the following table. P Data for Exercise 11.13 Antidote A B C D 1 0.31 0.82 0.43 0.45 0.45 1.10 0.45 0.71 0.46 0.88 0.63 0.66 0.43 0.72 0.76 0.62 0.36 0.92 0.44 0.56 o 2 i 0.29 0.61 0.35 1.02 0.40 0.49 0.31 0.71 0.23 1.24 0.40 0.38 30.22 0.30 0.23 0.30 0.21 0.37 0.25 0.35 0.18 0.38 0.24 0.31 0.23 0.29 0.22 0.33

a. Complete the analysis of variance table, test for interaction, and test the marginal means hypotheses for main effects.

b. Construct the interaction plots and identify any possible sources of interaction.

e. Use the Scheffe criterion to examine differences in the marginal treatment means. Contrast these results with those obtained by using the separate- criterion.

d. Prepare a plot of residuals against predicted values.

e. The residual plot suggests the reciprocal transformation, z = 1/ Make this transformation, and repeat the analysis, noting the effect on the interaction plots. Section 11.1.5