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

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...

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Bibliographic Details
Published in:Mathematics (Basel) 2023-04, Vol.11 (9), p.1982
Main Authors: Ben-Shachar, Mattan S., Patil, Indrajeet, Thériault, Rémi, Wiernik, Brenton M., Lüdecke, Daniel
Format: Article
Language:English
Subjects:
Chi-square test
Chi-square tests
chi-squared test
Confidence intervals
Contingency tables
Cramer’s V
effect sizes
Fei
Food
Hypotheses
Mathematical research
Mathematics
Meat products
Phi
Probability
Programming languages
Software
Statistical analysis
Statistics
Variables
Veganism
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11091982