Power and sample size determinations for the Wilcoxon signed-rank test

Abstract

The problem of calculating power and sample size for the Wilcoxon signed-rank test is discussed. The exact variance large-sample method is examined and explicit formulas are derived for observations from uniform, normal and Laplace distributions. Numerical results are presented to evaluate the exact variance procedure and compare its performance with two simplified approximations that have been suggested in the statistical literature. From the simulation results, it is evident that the exact variance approach is more accurate than the two approximate methods. To facilitate practical use, tabulated values of the estimated sample sizes are provided.

Keywords:

• Large-sample approximation
• Nonparametric method
• One-sample location problem

Acknowledgements

The authors wish to thank the associate editor and a referee for their suggestions for improving the clarity of the exposition. The research of the second author was partially supported by National Science Council grant NSC-93-2118-M-033-002.