Popular software packages report four generalizations of the ANOVA F test when conducting a multivariate analysis of variance (MANOVA). The reported operating characteristics of these fours tests vary widely depending on which research article the reader chooses. Some studies report extremely high type I error rates for a particular test even under ideal assumptions of multivariate normality and homoskedasticity; other studies report rates near the nominal level despite violations of the model assumptions. This simulation study seeks to clarify this apparent contradiction by providing a systematic evaluation of the type I error rates of the four statistics used to test for a group effect in MANOVA.

翻译：流行软件包在进行多元方差分析（MANOVA）时会报告ANOVA F检验的四种推广形式。关于这四种检验的操作特征，不同研究文献的报告结果差异显著。部分研究指出，即便在多元正态性和方差齐性理想假设下，特定检验的第一类错误率也极高；而另一些研究则报告即使在违反模型假设的情况下，错误率仍接近名义水平。本模拟研究旨在通过系统评估MANOVA中用于检验分组效应的四种统计量的第一类错误率，澄清这一明显矛盾。