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.

非正态性与异方差性在实际应用中十分常见。针对非参数贝伦斯-费希尔问题（Behrens–Fisher problem）中的两样本比较问题，学界已提出多种检验方法，但尚无单一检验可适用于所有场景。本文提出将两种检验方法——基于秩的韦尔奇t检验（Welch t test）与布伦纳-蒙泽尔检验（Brunner–Munzel test）——整合至极大检验框架内。仿真研究表明，以置换检验（permutation test）形式实施的该极大检验能够控制一类错误率（type I error rate）并稳定检验效能。换言之，其在多种分布场景下均具备优良的检验效能特征，同时可适用于非均衡样本量情形。相较于单一检验方法，该极大检验展现出可接受的一类错误控制表现。