Pairwise comparisons for Levene-style variability parameters

Abstract

The simplest way to test for equality of scale in one-way data is to use the analysis of variance applied to absolute deviations from sample medians in place of the original data. This approach started by Levene (1960, using means instead of medians), appears in most statistical packages and is quite powerful for detecting heterogeneity of scale. However, researchers often want to know where the differences lie and some measure of effect for those differences. Here, the Closed Method of pairwise comparisons combined with F statistics on the absolute deviations is shown to be an excellent method for detecting differences. In addition, the Bonferroni method is combined with pairwise t-statistics to construct confidence intervals for pairwise differences in scale.

Keywords:

• Tests of scale
• Absolute deviations
• Closed Method
• Multiple comparisons

Acknowledgments

We appreciate the advice from Peter Westfall and Jason Hsu concerning the Closed Method.