Effect Size Converter (d, r, f, η², OR)
Meta-analyses, power analyses and literature reviews constantly require moving between effect size metrics: the paper reports η², your power tool wants f; you have an odds ratio, the meta-analysis needs d. Enter any single measure — Cohen's d, correlation r, Cohen's f, eta squared or an odds ratio — and read all equivalents at once, computed with the standard conversion formulas (Cohen 1988; Borenstein et al. 2009). Provide the two group sizes optionally to get the exact unequal-n correction for r and the small-sample corrected Hedges' g. The common language effect size (CLES) is included too — the probability that a randomly chosen member of one group scores higher than one from the other, often the most intuitive number to give a non-statistical audience.
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Frequently asked questions
How do I convert Cohen's d to r?
For equal group sizes: r = d / √(d² + 4). For example d = 0.8 gives r = .37. With unequal groups the 4 is replaced by (n₁+n₂)²/(n₁n₂) — enter your group sizes and the calculator applies the exact correction.
How do I convert eta squared to Cohen's f?
f = √(η² / (1 − η²)), and back: η² = f²/(1 + f²). This is the conversion you need to feed a published ANOVA result into a power analysis: η² = .06 corresponds to f = 0.25.
What is the difference between Cohen's d and Hedges' g?
Both express a mean difference in SD units, but d is slightly biased upward in small samples. Hedges' g applies the correction factor J = 1 − 3/(4df − 1); with n > 50 the difference is negligible. Meta-analyses conventionally report g.
How do I convert an odds ratio to Cohen's d?
d = ln(OR) × √3 / π (Borenstein et al.). An OR of 2 corresponds to d ≈ 0.38 — useful for combining binary and continuous outcomes in one meta-analysis. Note it assumes the underlying logistic model.