The construction of good change-over designs when there are fewer units than treatments

Abstract

This paper studies the situation in which each of t treatments is applied, one per time period, to n < t experimental units. Each unit experiences the direct effect of the treatment applied in the current period and the residual effect of the treatment applied in the previous period. A design which gives good sequences of treatments to the units is obtained by selecting a subset of the columns of either Williams squares (Williams, 1949) or squares constructed by a method described in the present paper.