Groupe d’études et de recherche en analyse des décisions

G-2004-32

Asymptotic Efficiencies of the Sign and the Wilcoxon Signed-Rank Tests for Cluster Correlated Data

In this paper, we study the Pitman asymptotic efficiencies of the sign and the Wilcoxon signed-rank tests for cluster correlated data. A general expression is derived for the efficiency and actual values are obtained for the normal and Student t distributions. 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 intracluster correlation is present. Interestingly, the sign test can even be more efficient than the Wilcoxon signed-rank test in some situations.

, 14 pages