On optimal two-period repeated measurements designs

Two-period repeated measurements designs for optimal estimation of treatment contrasts are studied in four fixed effects models: (I) with unit and period effects, (II) with unit effects only, (III) with period effects only, and (IV) with neither period nor unit effects. For each model, errors within each unit are assumed to be correlated. The problems of optimality when units are random are also addressed. Strongly balanced two-period repeated measurements designs of Cheng and Wu (1980) are found to be universally optimal for direct effects under all four models. A different class of designs is found to be universally optimal for residual effects under models I and II. Optimal designs for residual effects under models III and IV are found to be very sensitive to the magnitude of within unit correlation coefficient. In general, optimal designs for both direct and residual effects under models III and IV are more restrictive than those under models I and II.