Crossover Designs: Analysis and Optimality Using the Calculus for Factorial Arrangements

A. Cross-over designs Crossover designs are used in experimental situations where a number of experimental subjects are exposed to the treatments under study applied sequentially over a number of time periods. They are used in a broad spectrum of research areas, some early exam-ples being agriculture (Cochran, 1939), dairy husbandry (Cochran et. al, 1941), bioassay procedures (Finny, 1965), clinical trials (Grizzle, 1965), psychological experiments (Kep-pel, 1973), weather modification experiments (Mielke, 1974), tea-tasting experiments and other areas of research. The advantage of the crossover design is the cost and the interunit variability elim-ination while computing treatment effects. These designs have been shown to be cost efficient as compared to completely randomized designs or parallel designs, except in a few extreme cases. However, since each subject is receiving a sequence of treaments over time, in addition to the ‘direct ’ effect of a treatment in the period in which it is applied, a treatment may also have ‘carryover ’ effects in one more subsequent periods. The possible presence of these ‘carryover ’ effects complicates the analysis of data from these designs