Repeated Measurement Designs of Five Periods: Estimating the Parameter of Carryover Effects

This study investigates the derivation of optimal repeated measurement designs of two treatments, five periods, and n experimental units for carryover effects. The optimal designs are determined for cases where n = 0, 1 (mod 2). The adopted optimality criterion focuses on minimizing the variance of the estimated carryover effect, thereby ensuring maximum precision in parameter estimation and design efficiency. The results presented here extend and complement earlier research of Chalikias and Kounias on optimal two-treatment repeated measurement designs for a smaller number of periods, and are closely related to the more recent findings on optimal designs for direct effects. Overall, the present work contributes to the theoretical framework of optimal design methodology by providing new insights into the structure and efficiency of repeated measurement designs, particularly in the presence of carryover effects, and sets the ground for future extensions incorporating treatment–period interactions.