CROSSOVER DESIGNS IN THE PRESENCE OF CARRY-OVER EFFECTS FROM 2 FACTORS

Experiments, used in the telecommunications industry and elsewhere, ar e considered that involve the simultaneous application of levels of tw o unrelated factors, treatments and stimuli, to each of several subjec ts in a succession of time periods. The existence is suspected of carr yover effects of treatments and stimuli, in the period immediately fol lowing the period of their application. Methods are given for the cons truction of separate sequences of treatments and of stimuli; these met hods are based on the Latin squares of Williams and of Russell. In the resulting designs, the treatments and stimuli are either orthogonal o r nearly orthogonal, and the coincidence of the direct and carry-over effects of each factor is either balanced or nearly balanced. The effi ciencies of the designs are assessed by comparing the average variance s of elementary contrasts in the levels of each factor with appropriat e lower bounds.