Phi, Fei, Fo, Fum: Effect Sizes for Categorical Data That Use the Chi-Squared Statistic
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
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.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.079 | 0.106 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.003 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.002 | 0.000 |
| Open science | 0.004 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 0.006 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it