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Phi, Fei, Fo, Fum: Effect Sizes for Categorical Data That Use the Chi-Squared Statistic

Author

Listed:
  • Mattan S. Ben-Shachar

    (Independent Researcher, Ramat Gan 5228555, Israel)

  • Indrajeet Patil

    (Center for Humans and Machines, Max Planck Institute for Human Development, 13437 Berlin, Germany)

  • Rémi Thériault

    (Department of Psychology, Université du Québec à Montréal, Montréal, QC H2X 3P2, Canada)

  • Brenton M. Wiernik

    (Independent Researcher, Tampa, FL 33604, USA)

  • Daniel Lüdecke

    (Institute of Medical Sociology, University Medical Center Hamburg-Eppendorf, 20246 Hamburg, Germany)

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 χ 2 (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.

Suggested Citation

  • Mattan S. Ben-Shachar & Indrajeet Patil & Rémi Thériault & Brenton M. Wiernik & Daniel Lüdecke, 2023. "Phi, Fei, Fo, Fum: Effect Sizes for Categorical Data That Use the Chi-Squared Statistic," Mathematics, MDPI, vol. 11(9), pages 1-10, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:1982-:d:1130188
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    References listed on IDEAS

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    1. Michael S Rosenberg, 2010. "A Generalized Formula for Converting Chi-Square Tests to Effect Sizes for Meta-Analysis," PLOS ONE, Public Library of Science, vol. 5(4), pages 1-3, April.
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