Sequentially Counterbalanced Designs Formed from Two or More Latin Squares

Abstract

Experiments in which t treatments are applied to n experimental units or subjects, such that each subject receives a treatment in each of p consecutive time periods, are commonly called cross-over designs or change-over designs. In such experiments, observations may be affected by carry-over effects from previously administered treatments. One model used in such situations to describe the observed response variable includes terms for subjects, periods and direct treatment effects, and an additive term for first-order carry-over treatment effects which depend only on the treatment applied in the preceding period, together with a random error term. See Jones and Kenward (1989) for further details.