Small Sample Properties of the Wilcoxon Signed Rank Test with Discontinuous and Dependent Observations

Abstract

This Monte-Carlo study investigates sensitivity of the Wilcoxon signed rank test to certain assumption violations in small samples. Emphasis is put on within-sample-dependence, between-sample dependence, and the presence of ties. Our results show that both assumption violations induce severe size distortions and entail power losses. Surprisingly, these consequences do vary substantially with other properties the data may display. Results provided are particularly relevant for experimental settings where ties and within-sample dependence are frequently observed.