Optimal Crossover Designs for Comparing Mixed Carryover Effects

Abstract

In this paper we consider a variant of the traditional noncircular model for crossover designs. Instead of assuming that ea.Ch treatment - applied to an experimental unit imparts the same carryover effect regardless of the treatment applied to the next period on the same unit, we consider the model which assumes two types of carryover effects that extend from a period to the next period. One type is called self carryover effect when a treatment is followed by itself in the next period on the same unit and the other type is called mixed carryover effect when a treatment is followed by any other treatment in the next period. Such models are useful in sensory trials. Efficient estimation and testing of the direct treatment effects (imparted by the treatment itself on the experimental unit of application) as well as the carryover effects under different models are of interest to the practitioners from application and model building point of view and have been addressed by many researchers. In the present article the problem of identification of optimal designs for the estimation of the mixed carryover effects has been taken up. It is shown that under the self and mixed carryover model generalised Patterson's balanced designs (termed also totally balanced designs in the literature}, which are known to be universally optimal for the estimation of the direct treatment effects are also universally optimal for the estimation of the mixed carryover effects provided that the number of periods exceeds two. AMS (2000} Subject Classification : 62K05.