论文标题
默认的贝叶斯因素用于测试几个人口差异的（在）平等的因素
Default Bayes Factors for Testing the (In)equality of Several Population Variances
论文作者
论文摘要
在许多统计应用中，测试方差平等是一个重要问题。我们开发默认的贝叶斯因子测试，以评估两个或多个人口差异的平等，以及对人口差异是否等于特定值的测试。最终的测试可用于检查常用过程（例如$ t $检验或ANOVA）的假设，或直接测试有关方差的实质性假设。我们表明，我们的贝叶斯因素实现了许多逃亡者。研究人员可能已经指示假设，例如$σ_{1}^{2}>σ_{2}^{2} $，他们可能想扩展$ \ nathcal {h} _ {0} $具有无效的null-region，或者希望与假设相等的假设，例如$} $ {1}，例如，$} σ_{2}^{2}>（σ_{3}^{2}，σ_{4}^{2}）$。我们扩展了贝叶斯因子测试，以允许与拟议默认值的这些偏差，并在许多实际示例中进行说明。我们的过程在R件$ bfvartest $中实现。
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 $σ_{1}^{2} > σ_{2}^{2}$, 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 $σ_{1}^{2} = σ_{2}^{2} > (σ_{3}^{2}, σ_{4}^{2})$. 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 $bfvartest$.
