Tests for Differences in Dispersion Based on Quantiles

It is commonly known that the validity of the F test for testing differences in variability is highly sensitive to the assumption that the population distributions are normal. Hence there is a need for nonparametric tests that do not rely on the assumption of normal population distributions. Several nonparametric tests for testing differences in dispersion have been developed in the past 40 years. These include Mood's test, Klotz's test, and the Siegel-Tukey test. Unfortunately, many of these tests do not have a natural or easily calculated measure of dispersion associated with them. This article introduces a test for differences in dispersion based on quantiles that is easy to compute and readily comprehended by the casual user of statistics.