d_to_r: Convert Between _d_, _r_, and Odds Ratio

View source: R/convert_between_d_to_r.R

d_to_rR Documentation

Convert Between d, r, and Odds Ratio


Enables a conversion between different indices of effect size, such as standardized difference (Cohen's d), (point-biserial) correlation r or (log) odds ratios.


d_to_r(d, n1, n2, ...)

r_to_d(r, n1, n2, ...)

oddsratio_to_d(OR, log = FALSE, ...)

logoddsratio_to_d(logOR, log = TRUE, ...)

d_to_oddsratio(d, log = FALSE, ...)

d_to_logoddsratio(d, log = TRUE, ...)

oddsratio_to_r(OR, n1, n2, log = FALSE, ...)

logoddsratio_to_r(logOR, log = TRUE, ...)

r_to_oddsratio(r, n1, n2, log = FALSE, ...)

r_to_logoddsratio(r, n1, n2, log = TRUE, ...)


d, r, OR, logOR

Standardized difference value (Cohen's d), correlation coefficient (r), Odds ratio, or logged Odds ratio.

n1, n2

Group sample sizes. If either is missing, groups are assumed to be of equal size.


Arguments passed to or from other methods.


Take in or output the log of the ratio (such as in logistic models), e.g. when the desired input or output are log odds ratios instead odds ratios.


Conversions between d and OR is done through these formulae:

  • d = \frac{\log(OR)\times\sqrt{3}}{\pi}

  • log(OR) = d * \frac{\pi}{\sqrt(3)}

Converting between d and r is done through these formulae:

  • d = \frac{\sqrt{h} * r}{\sqrt{1 - r^2}}

  • r = \frac{d}{\sqrt{d^2 + h}}

Where h = \frac{n_1 + n_2 - 2}{n_1} + \frac{n_1 + n_2 - 2}{n_2}. When groups are of equal size, h reduces to approximately 4. The resulting r is also called the binomial effect size display (BESD; Rosenthal et al., 1982).


Converted index.


  • Borenstein, M., Hedges, L. V., Higgins, J. P. T., & Rothstein, H. R. (2009). Converting among effect sizes. Introduction to meta-analysis, 45-49.

  • Jacobs, P., & Viechtbauer, W. (2017). Estimation of the biserial correlation and its sampling variance for use in meta-analysis. Research synthesis methods, 8(2), 161-180. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/jrsm.1218")}

  • Rosenthal, R., & Rubin, D. B. (1982). A simple, general purpose display of magnitude of experimental effect. Journal of educational psychology, 74(2), 166.

  • Sánchez-Meca, J., Marín-Martínez, F., & Chacón-Moscoso, S. (2003). Effect-size indices for dichotomized outcomes in meta-analysis. Psychological methods, 8(4), 448.

See Also


Other convert between effect sizes: diff_to_cles, eta2_to_f2(), odds_to_probs(), oddsratio_to_riskratio(), w_to_fei()



r_to_oddsratio(0.4472136, log = TRUE)
oddsratio_to_d(1.813799, log = TRUE)

effectsize documentation built on Sept. 14, 2023, 5:07 p.m.