An experimental design in which each experimental unit is used with each treatment being studied. The simplest crossover trial uses two groups of experimental units (e.g. hospital patients), 1 and 2, and two treatments (e.g. medicines), A and B. The trial uses two equal-length time periods. In the first period, group 1 is assigned treatment A and group 2 is assigned treatment B. In the second period, the assignments are reversed.

Balaam's design uses four groups of patients to compare two treatments in two periods. The assignments are AA, AB, BA, and BB. However, a complication in all crossover trials, unless there is a protracted gap between the two periods, is that the treatment allocated in the first period may continue to have an effect (the carry-over effect) during the second period. More complex allocations aim to estimate these effects. An example—involving two treatments, four groups, and three time periods—is designed to help with the estimation of the carry-over effects:

 The analysis of such a design is not simple; from the statistician's viewpoint (though not the patient's) it would be preferable to minimize the carry-over effects by allowing an interval (the wash-out period) between successive treatments.