Comparing Medians: A Monte Carlo Study

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Abstract
Several procedures have been proposed for testing H0: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 H0 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.

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