Suppose a dermatologist wants to study the effectiveness of two different preparations of a skin lotion using two 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, combination of preparation and frequency of application) to each arm of each patient. Even though the patients have the same disease, there exists considerable variation 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 obtained this plan.
iv For the design given in (iii), outline the ANOVA table, giving sources of variation, d.f., and sum of squares.
v For the plan given in (iii), what is the variance of the estimates of the main effects and the interaction?

My Findings :-
Here experimental unit is one arm and factors are forms of application, preparation of skin lotion and subject. I am not getting how to include subjects as factors ? Can anybody please explain how to approach this question ?