Estimating the Power of the Two-Sample Wilcoxon Test for Location Shift

Abstract

Traditional methods for calculating the power of a statistical test for location shift require knowledge of the shape of the underlying probability distribution. The distribution shape, however, may be unknown. This paper describes a bootstrap methods for using observed data (or pilot data) to aproximate the power. No assumptions need be made about the shape of the underlying continuous probability distribution. Simulation evidence shows that, when applied to the Wilcoxon two-sample test for location shift, the suggested method is reliable. The evidence also shows that it is more accurate than and benchmark traditional approach. The bootstrap method is applied to a real-data example. The analysis demonstrates how the method can be used to determine sample sizes and how to choose the more powerful of two alternative tests for location shift.