The Wilcoxon Signed-Rank Test for Cluster Correlated Data

Abstract

In this paper, we adapt the Wilcoxon signed-rank test to the case of cluster correlated data. A simple modification of the estimator of the asymptotic variance is sufficient to obtain a valid asymptotic procedure. However, the resulting test is no longer distribution-free. We derive the asymptotic null distribution of the statistic. A simulation study is performed in order to investigate the finite sample performance of the test. The results show that the performance of the test is very good for all designs and distributions considered when compared to competitors based on signs and on the overall average. In fact, the test is as powerful as the one based on the overall average for normal data as soon as intracluster correlation is present. An example of application with a real data set is also given.