Analysis of proportions using arcsine transform with any experimental design

Exact tests on proportions exist for single-group and two-group designs, but no general test on proportions exists that is appropriate for any experimental design involving more than two groups, repeated measures, and/or factorial designs.

Herein, we extend the analysis of proportions using arcsine transform to any sort of design. The resulting framework, which we have called Analysis of Proportions Using Arcsine Transform (ANOPA), is completely analogous to the analysis of variance for means of continuous data, allowing the examination of interactions, main and simple effects, post-hoc tests, orthogonal contrasts, et cetera.

We illustrate the method with a few examples (single-factor design, two-factor design, within-subject design, and mixed design) and explore type I error rates with Monte Carlo simulations. We also examine power computation and confidence intervals for proportions.

ANOPA is a complete series of analyses for proportions, applicable to any design.