Repeated Measurements and Cross-Over Designs

Chapter 8Other Cross-Over Designs with Residual Effects

8.1 INTRODUCTION

Standard CODWRs were discussed in Chapters 6 and 7. By changing the requirements of the design or modifying the assumptions, several useful new CODWR can be developed, and some of these results are given in this chapter.

In BRED, it was noted that the direct effects treatment contrasts are more efficiently estimated than the residual effects treatment contrasts. In order to reduce the differences in these variances, Lucas (1957) introduced extra-period cross-over designs in which the last period of Williams’ BRED is repeated for an extra period. This additional period makes the design orthogonal in estimating direct effects and residual effects of treatments. In this extra-period design, the residual effect of a treatment on itself may or may not be equal to the residual effect of the treatment on other treatments. These results will be discussed in Section 8.2. In some situations, we can assume that the residual effects are proportional to direct effects of the treatments. The analysis under this assumption will be given in Section 8.3.

While residual effects of different orders are usually different, in some settings, they may all be assumed equal. Consider the example of an interview in a survey setting. Each question of the schedule creates some kind of residual effect for answering the next question by the respondent. Since the interview period is usually short, the residual effect of answering each ...