propes: Proportions to Effect Size
Description
Converts proportions (typically seen in studies reporting odds ratios) to an effect size of $d$ (mean difference), $g$ (unbiased estimate of $d$), $r$ (correlation coefficient), $z'$ (Fisher's $z$), and log odds ratio. The variances of these estimates are also computed.Usage
propes(p1, p2, n.ab, n.cd)
Arguments
n.ab
Total sample size for group A and B.
n.cd
Total sample size for group C and D.
Value
- dStandardized mean difference ($d$).
- var.dVariance of $d$.
- gUnbiased estimate of $d$.
- var.gVariance of $g$.
- rCorrelation coefficient.
- var.rVariance of $r$.
- log.oddsLog odds ratio.
- var.log.oddsVariance of log odds ratio.
- nTotal sample size.
Details
This formula will first compute an odds ratio and then transform to log odds and its variance. Then, Cohen's $d$ will be calculated and this value will then be used to compute the remaining effect size estimates. The odds ratio is derived as follows
$$or= \frac{p_{1}(1-p_{2})} {p_{2}(1-p_{1})}$$
The conversion to a log odds and its variance is defined as
$$ln(o)= log(or)$$
$$v_{ln(o)}= \frac{1} {n_{AB}p_{1}(1-p_{1})}+ \frac{1} {n_{CD}p_{2}(1-p_{2})}$$
where $n_{AB}$ is the sum of group A and B sample size, $n_{CD}$ is the sum of group C and D sample size, $p_{1}$ is the proportion for group 1 and $p_{2}$ is the proportion for group 2.References
Borenstein (2009). Effect sizes for continuous data. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 279-293). New York: Russell Sage Foundation.