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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 &amp; Sen’s L statistic, Brunner &amp; Munzel’s ATS, the χ 2 -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 &amp; Sen’s L statistic, Brunner &amp; 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.

ANOVA with binary variables: the F-test and some alternatives