Calculate and interpret effect sizes for statistical analyses. Use when: (1) Reporting research results to show practical significance, (2) Meta-analysis to combine study results, (3) Grant writing to justify expected effects, (4) Interpreting published studies beyond p-values, (5) Sample size planning for power analysis.
View on GitHubastoreyai/ai_scientist
research-assistant
January 20, 2026
Select agents to install to:
npx add-skill https://github.com/astoreyai/ai_scientist/blob/main/skills/effect-size/SKILL.md -a claude-code --skill effect-sizeInstallation paths:
.claude/skills/effect-size/# Effect Size Calculation Skill ## Purpose Calculate standardized effect sizes to quantify the magnitude of research findings. Essential for reporting practical significance beyond p-values. ## Common Effect Size Measures ### Cohen's d (Mean Differences) **Use:** T-tests, group comparisons on continuous outcomes ``` d = (M₁ - M₂) / SD_pooled Interpretation: - Small: d = 0.2 - Medium: d = 0.5 - Large: d = 0.8 ``` ### Pearson's r (Correlations) **Interpretation:** - Small: r = 0.10 - Medium: r = 0.30 - Large: r = 0.50 ### Eta-squared (η²) and Partial Eta-squared (η²ₚ) **Use:** ANOVA, variance explained ``` η² = SS_effect / SS_total η²ₚ = SS_effect / (SS_effect + SS_error) Interpretation: - Small: η² = 0.01 - Medium: η² = 0.06 - Large: η² = 0.14 ``` ### Odds Ratio (OR) and Risk Ratio (RR) **Use:** Binary outcomes, clinical trials ``` OR = (a/b) / (c/d) [from 2x2 table] Interpretation: - OR = 1: No effect - OR > 1: Increased odds - OR < 1: Decreased odds ``` ## Always Report with Confidence Intervals ``` Example: d = 0.52, 95% CI [0.28, 0.76] This shows: - Best estimate: d = 0.52 (medium effect) - Precision: CI width suggests adequate sample size - Excludes zero: Effect is statistically significant ``` ## Integration Use with power-analysis skill for study planning and with statistical analysis for results reporting. --- **Version:** 1.0.0