Two-Stage Wilcoxon Tests of Hypotheses

Abstract

Two-stage Wilcoxon signed ranks tests and Wilcoxon-Mann-Whitney tests are presented for general one-sided alternatives. A probability recurrence relation is given for the two-stage signed ranks statistics under the null hypothesis. For each test the limiting bivariate distribution of the standardized statistics is normal. With certain restrictions on the sample sizes, the null limiting distributions are both the one considered by Owen [8], so large sample tests can be formed using existing tables. Monte Carlo results suggest that these tests can considerably reduce the expected number of observations without reducing power relative to the usual one-stage tests.