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skills/effect-size/SKILL.md

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+---
+name: effect-size
+description: "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."
+allowed-tools: Read, Write
+version: 1.0.0
+---
+
+# 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