| 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
