The Wilcoxon Signed-rank Test for Cluster Correlated Data

• Activity Number: 113
• Type: Contributed
• Date/Time: Monday, August 9, 2004 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Denis Larocque*+
• Companies: HEC Montréal
• Keywords: sign test ; one-sample location problem ; Wilcoxon signed-rank test ; intraclass correlation ; one-way random effect ; clustered observations

Abstract

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. We also study the Pitman asymptotic efficiency of the test and of the sign test. It is shown that for the normal and t distributions, the sign and Wilcoxon signed-rank tests always get better compared to an average based test as soon as intra-cluster correlation is present. Interestingly, the sign test can even be more efficient than the Wilcoxon signed-rank test in some situations. A simulation study is performed in order to investigate the finite sample performance of the tests. The results show that the performance of the Wilcoxon signed-rank 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 intra-cluster correlation is present.