A studentized permutation test for the nonparametric Behrens-Fisher problem in paired data

Abstract

We consider nonparametric ranking methods for matched pairs, whose distributions can have different shapes even under the null hypothesis of no treatment effect. Although the data may not be exchangeable under the null, we investigate a permutation approach as a valid procedure for finite sample sizes. In particular, we derive the limit of the studentized permutation distribution under alternatives, which can be used for the construction of $(1-\alpha)$-confidence intervals. Simulation studies show that the new approach is more accurate than its competitors. The procedures are illustrated using a real data set.