Convert between effect sizes
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Effect-size, power, and test-selection templates & worked examples from the Statistical Test Selection Workbook. We’ll email you the download link.
How effect size conversion works
Different fields report different effect-size metrics, but for a two-group comparison they describe the same thing and convert into one another. The conversions below treat Cohen’s d as the hub:
- d ↔ r: r = d / √(d² + 4), and d = 2r / √(1 − r²).
- d ↔ OR: ln(OR) = d × π/√3 (Cox/Chinn logit method).
- r ↔ η²: η² = r² for a two-group comparison.
Rough benchmarks (Cohen): d ≈ 0.2 / 0.5 / 0.8 and r ≈ 0.1 / 0.3 / 0.5 for small / medium / large. Always interpret against what is meaningful in your field, not the labels alone.
Conversions assume roughly equal group sizes (and, for OR, a logistic latent variable). Use them for reporting and meta-analysis; compute the effect size directly when you have raw data.
Frequently asked questions
How do I convert Cohen’s d to r?
For two equal groups, r = d / √(d² + 4); reverse with d = 2r / √(1 − r²).
How do I convert an odds ratio to d?
d = ln(OR) × √3/π (≈ ln(OR) × 0.5513). Reverse: OR = exp(d × π/√3) ≈ exp(d × 1.814).
What is η²?
The proportion of variance explained. For a two-group comparison η² = r². Benchmarks: ≈ 0.01 / 0.06 / 0.14 for small / medium / large.
Are the conversions exact?
They are standard approximations (equal groups; logistic latent variable for OR) — accurate enough for reporting and meta-analysis, not a substitute for computing from raw data.
Does it store anything?
No. Everything runs in your browser; nothing is uploaded or saved.