Data from: A non-parametric maximum test for the Behrens–Fisher problem

Non-normality and heteroscedasticity are common in applications. For the comparison of two samples in the non-parametric Behrens–Fisher problem, different tests have been proposed, but no single test can be recommended for all situations. Here, we propose combining two tests, the Welch t test based on ranks and the Brunner–Munzel test, within a maximum test. Simulation studies indicate that this maximum test, performed as a permutation test, controls the type I error rate and stabilizes the power. That is, it has good power characteristics for a variety of distributions, and also for unbalanced sample sizes. Compared to the single tests, the maximum test shows acceptable type I error control.

非正态性（non-normality）与异方差性（heteroscedasticity）在实际应用场景中十分常见。针对非参数贝伦斯-费希尔问题（non-parametric Behrens–Fisher problem）下的两样本比较任务，学界已提出多种检验方法，但尚无单一检验可适配所有应用情形。本文提出将基于秩的韦尔奇t检验（Welch t test based on ranks）与布伦纳-蒙策尔检验（Brunner–Munzel test）两种检验方法整合为一个最大检验。模拟研究结果显示，作为置换检验（permutation test）实施的该最大检验，能够有效控制一类错误率（type I error rate）并稳定检验效能。换言之，该检验在多种分布场景以及非均衡样本量（unbalanced sample sizes）条件下均具备优良的检验效能特性。相较于单一检验方法，该最大检验的一类错误控制表现处于可接受范围内。