A bootstrap test for equality of variances

TL;DR

This paper presents a bootstrap-based statistical test for assessing whether multiple variances are equal, offering improved error control over existing methods through simulation validation.

Contribution

It introduces a novel bootstrap procedure for testing equality of variances, derived from a normal-theory framework, with a new box-type acceptance region.

Findings

The method outperforms Shoemaker and Levene tests in error control.

Simulation shows better Type I and II error rates.

The test is generally superior to existing variance equality tests.

Abstract

We introduce a bootstrap procedure to test the hypothesis $H_o$ that $K+1$ variances are homogeneous. The procedure uses a variance-based statistic, and is derived from a normal-theory test for equality of variances. The test equivalently expressed the hypothesis as $H_o: \mathbf{\eta}=( \eta_1,\ldots,\eta_{K+1})^T=\mathbf{0}$, where $\eta_i$'s are log contrasts of the population variances. A box-type acceptance region is constructed to test the hypothesis $H_o$. Simulation results indicated that our method is generally superior to the Shoemaker and Levene tests, and the bootstrapped version of Levene test in controlling the Type I and Type II errors.