Abstract

Several methods to perform an ANOVA with a binary dependent variable in 2-way layouts are compared with the parametric F-test. Equal and unequal cell counts as well as several different effect models are taken into account. Special attention has been paid to heterogeneous conditions, which are caused by nonnull effects through the relation of the binomial probability and its variance. For between subject designs Puri & Sen’s L statistic, Brunner & Munzel’s ATS, the χ²-test of log-linear models, the logistic and the probit regresssions are considered. The L statistic is recommended, because the F-test cannot keep always the type I error under control, if there are nonnull effects. For mixed designs the Huynh-Feldt adjustment, Hotelling Lawley’s multivariate test, Puri & Sen’s L statistic, Brunner & Munzel’s ATS, Koch’s ANOVA, GLMM and GEE models are considered. None of these methods is able to cover all situations. Depending on the design and on the model to be checked, in most cases the parametric F-test with adjustment, the multivariate test or Koch’s method are advised. Additional results: heterogeneous correlations and the size of the design have an impact, particularly on the F-test.

摘要

将在 2 向布局中使用二元因变量执行方差分析的几种方法与参数 F 检验进行了比较。考虑了相等和不相等的细胞计数以及几种不同的效应模型。通过二项概率及其方差的关系，特别注意了由非零效应引起的异质条件。对于主题设计之间的 Puri & Sen 的 L 统计、Brunner & Munzel 的 ATS、χ ²- 对数线性模型的测试，逻辑和概率回归被考虑。建议使用 L 统计量，因为如果存在非零效应，F 检验无法始终控制 I 类错误。对于混合设计，考虑了 Huynh-Feldt 调整、Hotelling Lawley 的多变量检验、Puri & Sen 的 L 统计量、Brunner & Munzel 的 ATS、Koch 的方差分析、GLMM 和 GEE 模型。这些方法都无法涵盖所有​​情况。根据设计和要检查的模型，在大多数情况下，建议使用带调整的参数 F 检验、多变量检验或 Koch 方法。附加结果：异质相关性和设计的规模有影响，特别是对 F 检验。