Repeated Measurements and Cross-Over Designs

Chapter 6Cross-Over Designs with Residual Effects

6.1 INTRODUCTION

In Chapter 1 and Section 5.1, it was indicated that when a sequence of treatments are applied on an experimental unit over several periods and if no washout period can be left between successive periods, the analysis of the design has to be carried by taking into account the residual effects in the assumed linear model. It was further indicated that the direct effect of the treatment is the effect of the treatment manifested in the period of its application and ith-order residual effect is the residual effect of the treatment in the ith period after the treatment’s application is discontinued. While it is possible that the residual effects of all orders may be the same and this will be discussed in Section 8.2, in most designs, the residual effects of second and higher orders will be negligible and cross-over designs with first-order residual effects (CODWR) will be discussed in this chapter.

Since the treatments are applied to the experimental units without a break in CODWR, it becomes desirable to make allowance for a unit to be untreated in some periods. In the most general case of CODWR, one can consider b experimental units used over a k period experiment where in each period a unit may or may not receive one of the v treatments 1, 2, …, v. The setting can be written as a k × b array using v treatments. Let N = (n_ij) be a k × b matrix where n_ij = 1 or 0 according as the jth unit receives a treatment or ...