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

## Usage

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, ...)

## Arguments

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.

log

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.

Converted index.

## Details

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).

## References

• 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. 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.

cohens_d()

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

## Examples

r_to_d(0.5)
#> [1] 1.154701
d_to_oddsratio(1.154701)
#> [1] 8.120534
oddsratio_to_r(8.120534)
#> [1] 0.5000001

d_to_r(1)
#> [1] 0.4472136
r_to_oddsratio(0.4472136, log = TRUE)
#> [1] 1.813799
oddsratio_to_d(1.813799, log = TRUE)
#> [1] 0.9999998