The Wilcoxon-Mann-Whitney (WMW) test is the most commonly used nonparametric method to compare two treatments when the underlying distribution of the outcome variable is not normally distributed. In the presence of stratum effects, the van Elteren (vE) test, a stratified WMW test, can be used to adjust for the stratum effect. We provide guidance on how to choose between the two tests in the design phase of clinical trials and in the analysis of clinical data. We show by simulations that both tests preserve the type I error rate regardless of the presence of the stratum effects. Therefore, the test with greater power is preferred. In comparing powers, we found that the WMW test is better when the stratum effects are small, whereas the vE test is better when the stratum effects are large. Finally, when the stratum effects are moderate, the decision depends on the shape of the distribution and the ratio of the number of strata and the number of subjects. In this case, results presented in this article or from similar simulations may be used to determine which test is better.