Two-Sample Inference Based on One-Sample Wilcoxon Signed Rank Statistics

摘要

A two-sample test is studied which rejects the null hypothesis of equal population medians when two Wilcoxon distribution free confidence intervals are disjoint. A confidence interval for the difference in population medians is constructed by subtracting the endpoints of two one-sample confidence intervals. Two different ways to select the one-sample intervals are presented. A solution that specifies equal confidence coefficients for the one-sample intervals is recommended. All solutions are shown to have the same asymptotic (Pitman) efficiency as the Mann-Whitney two-sample test. Keywords: Mann-Whitney-Wilcoxon test; Nonparametric test; and Nonparametric confidence intervals.