Choosing cross-over designs when few subjects are available

Cross-over designs are used extensively for experiments in many fields. If the n subjects are relatively scarce compared to the t treatments then universally optimal designs do not exist under these restrictions and a computational procedure is usually required to select the design. This arises, for example, if the subjects comprise several animals which are in short supply, due perhaps to weight or age limitations. It is shown that cyclic cross-over designs are available that have lower average variances for direct and carry-over elementary treatment contrasts than other cyclic cross-over designs described in the literature. Examples of these improved designs are given for typical values of t and n. It is further shown that in these circumstances it is sensible to guard against a choice of design that can become disconnected if a few observations are lost during the experimentation. These points are illustrated in detail by considering the selection of a cross-over design for an experiment involving seven treatments applied to four subjects.