Optimal Designs for Direct Effects: The Case of Two Treatments and Five Periods

Abstract

Cross-Over Designs or Repeated Measurements Designs are experimental designs in which treatments (e.g., medicines, fertilizers, diets) are applied to experimental units (usually humans) in different time periods. A common problem is to find the distribution of n experimental units in order to find the optimal experimental design for the well-known criteria of optimality (A, D, E optimality, etc.). If there is only one parameter of interest, the criterion is the minimization of the variance of the parameter estimator. In this case, a Repeated Measurements Design with one parameter of interest (the direct effect of the treatment) is examined and the distribution of n which minimizes the variance of that parameter is found. The objective of the research is the estimation of the variance of the Ordinal Least-Squares estimators of the Repeated Measurements Design model for two treatments and five periods. Heydayat and Afsarinejad introduced the basic model which is used. The optimal Repeated Measurements Designs are derived for n experimental units. Optimality criterion is the minimization of the variance of the estimated direct effects.