Let $\{X_1,\ldots,X_m \}$ and $\{Y_1, \ldots, Y_n \}$ be two samples
independent of each other, but the random variables within each sample
are stationary associated with one dimensional marginal distribution
functions $F$ and $G$, respectively. We study the properties of the
classical Wilcoxon-Mann-Whitney statistic for testing for stochastic
dominance in the above set up.