A two-stage Wilcoxon-type nonparametric test for stochastic ordering in two samples

The Wilcoxon rank-sum test is a well-known nonparametric test for the equality of two distributions. In this article, we study a two-stage nonparametric procedure by first testing symmetry for the two underlying distributions and then using the Wilcoxon-type precedence test based on right-censored samples. Specifically, in the first stage, we use a test of symmetry for the two underlying distributions. Then, in the second stage, the minimal Wilcoxon rank-sum precedence test based on a partial sample is used for testing the equality of the two distributions against the stochastically ordered alternative, in which the size of the partial sample is determined by the outcome in the first stage. A simulation study reveals that the proposed two-stage procedure maintains the nominal level of significance and performs better than the classical Wilcoxon rank-sum test in terms of power in many situations. Finally, a numerical example is presented to illustrate the nonparametric procedures developed here.