A review of effect sizes and their confidence intervals, Part I: The Cohen's d family
Bibliographic record
Abstract
Effect sizes and confidence intervals are important statistics to assess the magnitude and the precision of an effect. The various standardized effect sizes can be grouped in three categories depending on the experimental design: measures of the difference between two means (the d family), measures of strength of association (e.g., r, R 2 , 2 , 2 ), and risk estimates (e.g., odds ratio, relative risk, phi; Part I of this study reviews the d family, with a special focus on Cohen's d and Hedges' g for two-independent groups and two-repeated measures (or paired samples) designs. The present paper answers questions concerning the d family via Monte Carlo simulations. First, four different denominators are often proposed to standardize the mean difference in a repeated measures design. Which one should be used? Second, the literature proposes several approximations to estimate the standard error. Which one most closely estimates the true standard deviation of the distribution? Lastly, central and noncentral methods have been proposed to construct a confidence interval around d. Which method leads to more precise coverage, and how to calculate it? Results suggest that the best way to standardize the effect in both designs is by using the pooled standard deviation in conjunction with a correction factor to unbias d. Likewise, the best standard error approximation is given by substituting the gamma function from the true formula by its approximation. Lastly, results from the confidence interval simulations show that, under the normality assumption, the noncentral method is always superior, especially with small sample sizes. However, the central method is equivalent to the noncentral method when n is greater than 20 in each group for a between-group design and when n is greater than 24 pairs of observations for a repeated measures design. A practical guide to apply the findings of this study can be found after the general discussion.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.101 | 0.315 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.006 | 0.005 |
| Bibliometrics | 0.025 | 0.018 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.005 | 0.009 |
| Open science | 0.006 | 0.003 |
| Research integrity | 0.005 | 0.007 |
| Insufficient payload (model declined to judge) | 0.006 | 0.003 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".