AUTHOR=Laurencelle Louis , Cousineau Denis 

TITLE=Analysis of proportions using arcsine transform with any experimental design

JOURNAL=Frontiers in Psychology

VOLUME=13

YEAR=2023

URL=https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2022.1045436

DOI=10.3389/fpsyg.2022.1045436

ISSN=1664-1078

ABSTRACT=<sec><title>Introduction</title><p>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.</p></sec><sec><title>Method</title><p>Herein, we extend the analysis of proportions using arcsine transform to any sort of design. The resulting framework, which we have called <italic>Analysis of Proportions Using Arcsine Transform</italic> (ANOPA), is completely analogous to the analysis of variance for means of continuous data, allowing the examination of interactions, main and simple effects, <italic>post-hoc</italic> tests, orthogonal contrasts, et cetera.</p></sec><sec><title>Result</title><p>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.</p></sec><sec><title>Discussion</title><p>ANOPA is a complete series of analyses for proportions, applicable to any design.</p></sec>