Converts $d$ (mean difference) to an effect size of $g$ (unbiased estimate of $d$), $r$ (correlation coefficient), $z$ (Fisher's $z$), and log odds ratio. The variances of these estimates are also computed.
Usage
des(d, n.1, n.2)
Arguments
d
Mean difference statistic ($d$).
n.1
Sample size of group one.
n.2
Sample size of group one.
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
Information regarding input (d):
In a study comparing means from independent groups, the population standardized mean difference is defined as
$$\delta= \frac{\mu_{2}-\mu_{1}} {\sigma}$$
where $\mu_{2}$ is the population mean of the second group, $\mu_{1}$ is the population mean of the first group, and $\sigma$ is the population standard deviation (assuming $\sigma_{2}$ = $\sigma_{1}$).
The estimate of $\delta$ from independent groups is defined as
$$d= \frac{\bar Y_{2}-\bar Y_{1}} {S_{within}}$$
where $\bar Y_{2}$ and $\bar Y_{1}$ are the sample means in each group and $S_{within}$ is the standard deviation pooled across both groups and is defined as
$$S_{within}= \sqrt{\frac{(n_{1}-1)S^2_{1}+(n_{2}-1)S^2_{2}} {n_{1}+n_{2}-2}}$$
where $n_{1}$ and $n_{2}$ are the sample sizes of group 1 and 2 respectively and $S^2_{1}$ and $S^2_{2}$ are the standard deviations of each group. The variance of $d$ is then defined as
$$v_{d}= \frac{n_{1}+n_{2}} {n_{1}n_{2}}+ \frac{d^2} {2(n_{1}n_{2})}$$
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.