# d_to_r: Convert Between _d_, _r_, and Odds Ratio In effectsize: Indices of Effect Size

 d_to_r R Documentation

## Convert Between d, r, and Odds Ratio

### Description

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

### Usage

```d_to_r(d, ...)

r_to_d(r, ...)

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

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

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

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

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

r_to_oddsratio(r, log = FALSE, ...)
```

### Arguments

 `d` Standardized difference value (Cohen's d). `...` Arguments passed to or from other methods. `r` Correlation coefficient r. `OR` Odds ratio values in vector or data frame. `log` Take in or output the log of the ratio (such as in logistic models).

### 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 = 2 * r / sqrt(1 - r^2)

• r = d / sqrt(d^2 + 4)

The conversion from d to r assumes equally sized groups. The resulting r is also called the binomial effect size display (BESD; Rosenthal et al., 1982).

Converted index.

### References

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

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

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

`cohens_d()`

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

### 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)

```

effectsize documentation built on Oct. 31, 2022, 5:06 p.m.