Comparing Medians: A Monte Carlo Study

Abstract

Several procedures have been proposed for testing H ₀:θ _x = θ _y . where θ _x and θ _y are the medians corresponding to two independent treatment groups. Unfortunately, most of these procedures have been found to be inadequate. For a variety of distribution shapes, this paper compares the performance of three large-sample tests of H ₀ for sample sizes ranging from 11 to 25. Although two of these procedures are simple extensions of existing results, they have not been previously considered in terms of testing θ _x = θ _y . The method that gave the best results is based on a normal approximation of the distribution of the sample median where the variance is estimated using results reported by Maritz and Jarrett (1978). The Fligner-Rust procedure is found to be inadequate in situations not considered in previous investigations, but it performs well when the sample sizes are equal and reasonably large.