Two modified Wilcoxon tests for symmetry about an unknown location parameter

Abstract

SUMMARY Two modifications of the Wilcoxon test for symmetry about the sample median are proposed and their large sample distribution theory derived. Their Pitman efficacies against contamination in the right tail are obtained. Both the asymptotic results and a Monte Carlo study show that the procedures are more powerful than the Wilcoxon test about the median against many asymmetric alternatives while preserving its robustness of level shown by Antille & Kersting (1977).