d_to_r() R function from [effectsize]

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, p0, log = FALSE, ...)

logoddsratio_to_d(logOR, p0, log = TRUE, ...)

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

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

oddsratio_to_r(OR, p0, n1, n2, log = FALSE, ...)

logoddsratio_to_r(logOR, p0, n1, n2, 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.
p0: Baseline risk. If not specified, the d to OR conversion uses am approximation (see details).
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.

Returns

Converted index.

Details

Conversions between d and OR is done through these formulae:

$d = log(OR) * sqrt(3) / pi$
$log(OR) = d * pi / sqrt(3)$

Converting between d and r is done through these formulae:

$d = sqrt(h) * r / sqrt(1 - r^2)$
$r = d / sqrt(d^2 + h)$

Where $h = (n1 + n2 - 2) / n1 + (n1 + n2 - 2) / n2$ . When groups are of equal size, h reduces to approximately 4. The resulting ris also called the binomial effect size display (BESD; Rosenthal et al., 1982).

Examples


r_to_d(0.5)
d_to_oddsratio(1.154701)
oddsratio_to_r(8.120534)

d_to_r(1)
r_to_oddsratio(0.4472136, log = TRUE)
oddsratio_to_d(1.813799, log = TRUE)

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. 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.

d_to_r function