Factorial designs lend themselves to a variety of analyses with Bayesian methodology. The de facto standard is Bayesian analysis of variance (ANOVA) with Monte Carlo integration. Alternative, and readily available methods, are Bayesian ANOVA with Laplace approximation as well as Bayesian t tests for individual effects. This simulation study compared the three approaches regarding ordinal and metric agreement of the resulting Bayes factors for a 2 × 2 mixed design. Simulation results indicate remarkable disagreement of the three methods in certain cases, particularly when effect sizes are small and studies include small sample sizes. Findings further replicate and extend previous observations of substantial variability of ANOVAs with Monte Carlo integration across different runs of one and the same analysis. These observations showcase important limitations of current implementations of Bayesian ANOVA. Researchers should be mindful of these limitations when interpreting corresponding analyses, ideally applying multiple approaches to establish converging results. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

中文翻译：

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贝叶斯方差分析中贝叶斯因子估计的一致性。


因子设计适合使用贝叶斯方法进行各种分析。事实上的标准是采用蒙特卡罗积分的贝叶斯方差分析 (ANOVA)。另一种现成的方法是采用拉普拉斯近似的贝叶斯方差分析以及针对个体效应的贝叶斯 t 检验。该模拟研究比较了 2 × 2 混合设计中所得贝叶斯因子的序数和度量一致性的三种方法。模拟结果表明，在某些情况下，三种方法存在显着差异，特别是当效应量较小且研究样本量较小时。研究结果进一步复制和扩展了先前对方差分析的显着变异性的观察，其中蒙特卡罗积分在同一分析的不同运行中进行。这些观察结果展示了贝叶斯方差分析当前实施的重要局限性。研究人员在解释相应的分析时应注意这些局限性，最好应用多种方法来建立趋同的结果。 （PsycInfo 数据库记录 (c) 2024 APA，保留所有权利）。