77 lines
1.8 KiB
Markdown
77 lines
1.8 KiB
Markdown
---
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name: effect-size
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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."
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allowed-tools: Read, Write
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version: 1.0.0
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---
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# Effect Size Calculation Skill
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## Purpose
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Calculate standardized effect sizes to quantify the magnitude of research findings. Essential for reporting practical significance beyond p-values.
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## Common Effect Size Measures
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### Cohen's d (Mean Differences)
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**Use:** T-tests, group comparisons on continuous outcomes
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```
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d = (M₁ - M₂) / SD_pooled
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Interpretation:
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- Small: d = 0.2
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- Medium: d = 0.5
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- Large: d = 0.8
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```
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### Pearson's r (Correlations)
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**Interpretation:**
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- Small: r = 0.10
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- Medium: r = 0.30
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- Large: r = 0.50
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### Eta-squared (η²) and Partial Eta-squared (η²ₚ)
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**Use:** ANOVA, variance explained
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```
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η² = SS_effect / SS_total
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η²ₚ = SS_effect / (SS_effect + SS_error)
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Interpretation:
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- Small: η² = 0.01
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- Medium: η² = 0.06
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- Large: η² = 0.14
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```
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### Odds Ratio (OR) and Risk Ratio (RR)
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**Use:** Binary outcomes, clinical trials
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```
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OR = (a/b) / (c/d) [from 2x2 table]
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Interpretation:
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- OR = 1: No effect
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- OR > 1: Increased odds
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- OR < 1: Decreased odds
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```
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## Always Report with Confidence Intervals
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```
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Example: d = 0.52, 95% CI [0.28, 0.76]
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This shows:
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- Best estimate: d = 0.52 (medium effect)
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- Precision: CI width suggests adequate sample size
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- Excludes zero: Effect is statistically significant
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```
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## Integration
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Use with power-analysis skill for study planning and with statistical analysis for results reporting.
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---
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**Version:** 1.0.0
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