Two‐Sample Inference Based on One‐Sample Sign Statistics

A two‐sample test is studied which rejects the null hypothesis of equal population medians when two distribution‐free confidence intervals are disjoint. A confidence interval is constructed by subtracting the endpoints of the two one‐sample confidence Intervals. Three different ways to select the one‐sample Intervals are presented. Mood's median test is shown to be one of the solutions; however, an alternative solution that specifies equal confidence coefficients for the one‐sample intervals is recommended. All solutions are shown to have the same asymptotic efficiency.