TimelyScholarFree Tools › Effect Size Converter
Convert effect sizes so studies can be combined in one meta-analysis. Move between Cohen's d (SMD), odds ratios, log odds ratios, correlations and Fisher's z, with confidence intervals.
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| Cohen's d (SMD) | 0.500 (95% CI 0.200 to 0.800)SE 0.1531 |
|---|---|
| Log odds ratio | 0.907 (95% CI 0.363 to 1.451)SE 0.2776 |
| Odds ratio | 2.477 (95% CI 1.437 to 4.268) |
| Correlation r | 0.243 (95% CI 0.100 to 0.371)r² = 0.059 |
| Fisher's z | 0.247 (95% CI 0.100 to 0.390)SE 0.0740 (derived from the converted CI) |
d ↔ odds ratio assumes an underlying continuous outcome with a logistic distribution in both groups (ln OR = d × π/√3). d ↔ r treats r as a point-biserial correlation between group membership and the outcome.
d, odds ratio, log odds ratio or r.
Add its 95% CI to convert the interval too.
With standard errors for meta-analysis software.
Studies of the same question often report different effect measures. Converting them to a common metric lets you pool them, for example re-expressing odds ratios from dichotomised outcomes as standardised mean differences.
Converting an odds ratio to d assumes the underlying continuous outcome follows a logistic distribution with equal variance in both groups; the Cochrane Handbook describes multiplying the SMD by π/√3 (about 1.81) to obtain a log odds ratio.
Take the natural log of the odds ratio and multiply by √3/π (about 0.551). For OR = 2.5, d ≈ 0.51.
Yes, this is common practice, but state which studies were converted and consider a sensitivity analysis without them.