A two-sample distribution-free procedure is proposed for testing equal locations under a stochastic ordering restriction. The test statisticMis an estimator ofP(X≤Y) based upon maximum likelihood estimators of stochastically ordered distribution functions. Some properties of theMtest are developed and critical values are provided for selected sample sizes. A Monte Carlo power study indicates that theMtest is more effective (for shift alternatives) than the Mann-Whitney-Wilcoxon test when the form of the underlying distribution is heavy-tailed, but the Mann-Whitney-Wilcoxon is preferred for moderate-tailed distributions.