Choice between two treatments,AandB, is sometimes based on the probability thatAwill be more effective (score higher, say) thanB.Ideally, to estimate this probability a sample of subjects would receive bothAandBand the proportion of(A — B)differences which are positive would be used as the estimate. Often, however, both treatments cannot be given to each subject, and inference is based on a trial using two independent samples. Unfortunately, probability structures exist for whichP(A — B> 0) for two independent samples is not equal toP(A — B> 0) for matched samples. The two-independent-sample Wilcoxon test statistic addresses the former probability and hence cannot be used to answer the question, “Is the probability thatAwill do better thanBgreater than 1/2?” unless further assumptions are made.