ON COMPARING 2 TREATMENTS

Choice between two treatments, A and B, is sometimes based on the probability that A will be more effective (score higher, say) than B. Ideally, to estimate this probability a sample of subjects would receive both A and B and 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 which P(A - B > 0) for two independent samples is not equal to P(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 that A will do better than B greater than 1/2?" unless further assumptions are made.