In a one-way analysis-of-variance (ANOVA) model, the number of all pairwise comparisons can be large even when there are only a moderate number of groups. Motivated by this, we consider a regime with a growing number of groups, and prove that for testing pairwise comparisons the BH procedure can offer asymptotic control on false discoveries, despite that the t-statistics involved do not exhibit the well-known positive dependence structure called the PRDS to guarantee exact false discovery rate (FDR) control. Sharing Tukey's viewpoint that the difference in the means of any two groups cannot be exactly zero, our main result is stated in terms of the control on the directional false discovery rate and directional false discovery proportion. A key technical contribution is that we have shown the dependence among the t-statistics to be weak enough to induce a convergence result typically needed for establishing asymptotic FDR control. Our analysis does not adhere to stylized assumptions such as normality, variance homogeneity and a balanced design, and thus provides a theoretical grounding for applications in more general situations.

翻译：在单因素方差分析模型中，即使组数适中，所有成对比较的数量也可能很大。受此启发，我们考虑组数递增的框架，并证明在检验成对比较时，BH程序能够提供渐进的错误发现控制，尽管涉及的t统计量并不具备能保证精确错误发现率（FDR）控制的已知正相依结构PRDS。延续Tukey关于任意两组均值差不可能精确为零的观点，我们的主要结果以方向性错误发现率和方向性错误发现比例的控制形式呈现。关键技术贡献在于，我们证明了t统计量之间的相依性足够弱，能够导出通常用于建立渐近FDR控制的收敛性结果。我们的分析不依赖正态性、方差齐性和平衡设计等理想化假设，从而为更一般情形下的应用提供了理论基础。