Simultaneous comparisons of the variances of k treatments with that of a control: a Levene-Dunnett type procedure

TL;DR

This paper introduces a new statistical procedure for comparing variances of multiple treatments against a control, extending existing methods to pairwise variance comparisons using a Levene-Dunnett type approach, supported by simulations and R code.

Contribution

It proposes a novel Levene-Dunnett type test for pairwise variance comparisons in one-way layouts with a control, filling a gap in existing heterogeneity tests.

Findings

The method effectively detects variance differences in simulations.

The approach is demonstrated with real data examples.

R code implementation is provided for practical use.

Abstract

There are some global tests for heterogeneity of variance in k-sample one-way layouts, but few consider pairwise comparisons between treatment levels. For experimental designs with a control, comparisons of the variances between the treatment levels and the control are of interest - in analogy to the location parameter with the Dunnett (1955) procedure. Such a many-to-one approach for variances is proposed using the Levene transformation, a kind of residuals. Its properties are characterized with simulation studies and corresponding data examples are evaluated with R code.