ANOFA

Analyses of frequencies can be performed using an alternative test based on the G statistic. The test has similar type-I error rates and power as the chi-square test. However, it is based on a total statistic that can be decomposed in an additive fashion into interaction effects, main effects, simple effects, contrast effects, etc., mimicking precisely the logic of ANOVA. We call this set of tools 'ANOFA' (Analysis of Frequency data) to highlight its similarities with ANOVA. This framework also renders plots of frequencies along with confidence intervals. Finally, effect sizes and planning statistical power are easily done under this framework. The ANOFA is a tool that assesses the significance of effects instead of the significance of parameters; as such, it is more intuitive to most researchers than alternative approaches based on generalized linear models. See Laurencelle and Cousineau (2023) doi:10.20982/tqmp.19.2.p173.