A bootstrap test for equality of variances

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.