One-way analysis of variance (one-way ANOVA) is a statistical method used to compare means of more than two groups. ANOVA tests the null hypothesis that samples from different groups are drawn from populations with the same mean value. Typically it is used for continuous data and produces an F-statistic, the ratio of the variances calculated as the between-group variance to the within-group variance. When the responses/outcomes are binary or count data, the
assumptions of normality and equal variances are violated. Thus the conventional method of ANOVA is no longer reliable for binary or count data, and statistical power analysis based on conventional ANOVA is
incorrect. To address the issue, we first (1) produced a likelihood ratio test statistic through variation decomposition for one-way ANOVA with binary or count data. With the new test statistic, we then (2) defined the effect size and introduced the formula to calculate the statistical power. Finally, we (3) developed software to conduct the power analysis.