11.7 Suppose a dermatologist wants to study the effectiveness of two (2) different preparations of a skin lotion using two (2) different forms of application (for example, one vs. two applications per day). He has available 12 patients with a certain skin disease and he can apply one form of medication (that is, combi- nation of preparation and frequency of application) to each arm of each patient. Even though the patients have the same disease, there exists considerable varia- tion among them, but the two arms of a patient are quite homogeneous. (i) What type of experimental design would be appropriate for this study? (ii) What are the experimental units? (iii) Give a suitable experimental plan for this study and describe how you ob- tained this plan. (iv) For the design given in (iii), outline the ANOVA table, giving sources of variation, d.f., and sums of squares.

(v) For the plan given in (iii), what is the variance of the estimates of the main effects and the interaction?