Testing the (in)equality of variances is an important problem in many statistical applications. We develop default Bayes factor tests to assess the (in)equality of two or more population variances, as well as a test for whether the population variances equal a specific value. The resulting test can be used to check assumptions for commonly used procedures such as the $t$-test or ANOVA, or test substantive hypotheses concerning variances directly. We show that our Bayes factor fulfills a number of desiderata. Researchers may have directed hypotheses such as $\sigma_{1}^{2} > \sigma_{2}^{2}$, they may want to extend $\mathcal{H}_{0}$ to have a null-region, or wish to combine hypotheses about equality with hypotheses about inequality, for example $\sigma_{1}^{2} = \sigma_{2}^{2} > (\sigma_{3}^{2}, \sigma_{4}^{2})$. We extend our Bayes factor test to allow for these deviations from our proposed default and illustrate it on a number of practical examples. Our procedure is implemented in the R package $bfvartest$.
翻译：在很多统计应用中,测试差异的(不)平等是一个重要问题。我们开发了默认的贝叶因数测试,以评估两种或两种以上人口差异的(不)平等,并测试人口差异是否等于特定值。由此得出的测试可以用来检查通用程序的假设,如美元测试或ANOVA,或直接测试差异的实质性假设。我们显示,我们的贝叶因数符合一些偏差值。研究人员可能已经给出了诸如$\sigma ⁇ 1 ⁇ 2} >\gigma ⁇ 2 ⁇ 2}等假设,他们可能想要将$\mathcal{H ⁇ 0}扩大到一个无区域,或者希望将平等假设与不平等假设结合起来,例如$\sigma1 ⁇ 2}=\gma2 ⁇ 2} >(sigma3 ⁇ 2},\gma%4 ⁇ 2}。我们扩展了我们的贝因因因数测试,以允许这些偏离我们提议的违约值的美元/H ⁇ 2}。我们用一个实际例子来说明我们的成套程序。
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