Statistical tests for the overall hypothesis of no difference among multiple groups of a dichotomous response experiment include the likelihood ratio, Pearson'sX2, Goodman'sY2, and the analysis of variance (ANOVA)F. An empirical study is performed to evaluate these tests and the Bonferroni and maximal contrast methods of multiple comparisons for a four group experiment. TheFtest is recommended as an overall test and for maximal contrast comparisons, but its nominal significance level can be optimistic for certain Bonferroni comparisons with small samples. TheX2test is generally more conservative than theFtest.