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

Mattan S. Ben-Shachar, Indrajeet Patil, Rémi Thériault, Brenton M. Wiernik, Daniel Lüdecke

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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 (Formula presented.) (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.

Original languageEnglish
Article number1982
Issue number9
StatePublished - 1 May 2023


  • Cramer’s V
  • Fei
  • Phi
  • chi-squared test
  • effect sizes

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • General Mathematics
  • Engineering (miscellaneous)


Dive into the research topics of 'Phi, Fei, Fo, Fum: Effect Sizes for Categorical Data That Use the Chi-Squared Statistic'. Together they form a unique fingerprint.

Cite this