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2018•arXiv (Cornell University)Open access

A bootstrap test for equality of variances

Dexter Cahoy

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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 $H_o: \mathbfη=( η_1,\ldots,η_{K+1})^T=\mathbf{0}$, where $η_i$'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.

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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 $H_o: \mathbfη=( η_1,\ldots,η_{K+1})^T=\mathbf{0}$, where $η_i$'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.

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Available 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 $H_o: \mathbfη=( η_1,\ldots,η_{K+1})^T=\mathbf{0}$, where $η_i$'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.

Key concepts: F-test of equality of variances, Levene's test, Mathematics, Statistic, Statistics, Type I and type II errors, Homogeneous, Test (biology)

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