New methods for comparing the medians corresponding to independent treatment groups are suggested. Procedures are based on the estimator of F. Harrell and C. Davis in conjunction with a modification and extension of the bootstrap calibration technique suggested by W. Loh. Data from two groups provide an illustration. (SLD)

Modifications are proposed to the recently developed method of comparing one-step M-estimators of location corresponding to two independent groups that provides good control over the probability of Type I error even for unequal sample size, unequal variances, and different shaped distributions. Simulation results reveal cautions required. (SLD)