Phi, Fei, Fo, Fum: Effect sizes for categorical data that use the chi-squared statistic

Apr 20, 2023·
Mattan S. Ben-Shachar
,
Indrajeet Patil
Rémi Thériault
Rémi Thériault
,
Brenton M. Wiernik
,
Daniel Lüdecke
· 1 min read
Abstract
In both theoretical and applied research, it is often of interest to assess the strength of an observed association. Existing guidelines also frequently recommend going beyond null-hypothesis significance testing and reporting effect sizes and their confidence intervals. As such, measures of effect sizes are increasingly reported, valued, and understood. Beyond their value in shaping the interpretation of the results from a given study, reporting effect sizes is critical for meta-analyses, which rely on their aggregation. We review the most common effect sizes for analyses of categorical variables that use the χ2 (chi-square) statistic and introduce a new effect size—פ (Fei, pronounced “fay”). We demonstrate the implementation of these measures and their confidence intervals via the effectsize package in the R programming language.
Type
Publication
Mathematics, 11(9), 1982
publications

In both theoretical and applied research, it is often of interest to assess the strength of an observed association. Existing guidelines also frequently recommend going beyond null-hypothesis significance testing and reporting effect sizes and their confidence intervals. As such, measures of effect sizes are increasingly reported, valued, and understood. Beyond their value in shaping the interpretation of the results from a given study, reporting effect sizes is critical for meta-analyses, which rely on their aggregation. We review the most common effect sizes for analyses of categorical variables that use the χ2 (chi-square) statistic and introduce a new effect size—פ (Fei, pronounced “fay”). We demonstrate the implementation of these measures and their confidence intervals via the effectsize package in the R programming language.

Rémi Thériault
Authors
Rémi Thériault
Assistant Professor of Psychology and SAGE Lab Director
Rémi Thériault is an Assistant Professor of Psychology at the Université du Québec à Rimouski and director of the SAGE Lab. His research examines social identities, implicit cognition, prosociality, empathy, and self-regulation.