On occasion, the response to treatment in an AB/BA crossover trial is measured on a binary variable - success or failure. It is assumed that response to treatment is measured on an outcome variable with (+) representing a treatment success and a (-) representing a treatment failure. Traditionally, three tests for comparing treatment effect have been used (McNemar’s, Mainland-Gart, and Prescott’s). An issue arises concerning treatment comparisons when there may be a residual effect (carryover effect) of a previous treatment affecting the current treatment. A general consensus as to which procedure is preferable is debatable. However, if both group and carry-over effects are absent, Prescott’s test is the best one to use. Under a model with residual effects, Prescott’s test is biased. Therefore, a conservative approach includes testing for residual effects. When there is no period effect, McNemar’s test is optimal, while McNemar’s test is biased.