Summary and Practical Guide to Hypothesis Testing › Effect Size Reference
Michael BrenndoerferJanuary 10, 20262 min read
Machine Learning from ScratchAll chapters Part 2 of 9Hypothesis Testing
Summary and Practical Guide to Hypothesis Testing › Effect Size ReferenceOne section · Sections in this chapter4 / 12 ↓
Sections in this chapter12
Reading tools Definitions & inline links
Choose your expertise level to adjust how many terms are explained. Beginners see more tooltips, experts see fewer to maintain reading flow. Hover over underlined terms for instant definitions.
Article links
Make inline references clickable
Effect sizes quantify the magnitude of an effect independent of sample size. Always report them alongside p-values.
Cohen's d (Comparing Two Means)
| Cohen's d | Interpretation | Practical Example |
|---|---|---|
| 0.2 | Small | Subtle difference, requires large sample to detect |
| 0.5 | Medium | Noticeable effect, visible with moderate sample |
| 0.8 | Large | Substantial effect, obvious in most analyses |
| 1.2+ | Very large | Major effect, visible to naked eye |
Related measures:
- Hedges' g: Corrects d for small sample bias
- Glass's Δ: Uses control group SD only
- Cohen's d_z: For paired designs, uses SD of differences
ANOVA Effect Sizes
| Measure | Formula | Interpretation |
|---|---|---|
| η² (eta-squared) | % variance explained (biased upward) | |
| ω² (omega-squared) | Corrected formula | Less biased estimate |
| Partial η² | For factorial designs | Effect controlling for other factors |
Benchmarks for η² and ω²:
- Small: 0.01
- Medium: 0.06
- Large: 0.14
Correlation as Effect Size
| r | Interpretation | r² (variance explained) |
|---|---|---|
| 0.1 | Small | 1% |
| 0.3 | Medium | 9% |
| 0.5 | Large | 25% |