A class of statistics is introduced for testing stochastic ordering between two independent distributions. This class includes as a special case the celebrated Mann—Whitney—Wilcoxon statistic. The new class is shown to be asymptotically normal both under the null and nonnull hypotheses. It is distribution-free. Using Pitman's asymptotic efficacy it is shown that for some alternatives the Mann—Whitney—Wilcoxon statistic is the member with the highest efficacy, although for others it is not, and the member with the highest efficacy is identified.