Estimating the Parameter of Direct Effects in Crossover Designs: The Case of 6 Periods and 2 Treatments

The present study investigates the derivation of optimal repeated measurement designs for two treatments, six periods, and n experimental units, focusing exclusively on the direct effects of the treatments. The optimal designs are determined for cases where n ≡ 0 or 1, 2, 3, 4 (mod 4). The adopted optimality criterion aims at minimizing the variance of the estimator of the direct effects, thereby ensuring maximum precision in parameter estimation and increased design efficiency. The results presented extend and complement earlier studies on optimal two-treatment repeated-measurement designs for a smaller number of periods, and are closely related to more recent work focusing on optimality with respect to direct effects. Overall, this work contributes to the theoretical framework of optimal design methodology by providing new insights into the structure and efficiency of repeated measurement designs, and lays the groundwork for future extensions incorporating treatment–period interactions.