Converts binary data, that only reported the number of 'failure' groups, to $d$ (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
failes(B, D, n.1, n.0)
Arguments
B
Treatment failure.
D
Non-treatment failure.
n.1
Treatment sample size.
n.0
Control/comparison sample size.
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 a log odds and its variance. From there, Cohen's $d$ is computed and the remaining effect size estimates are then derived from $d$. Computing the odds ratio involves
$$or= \frac{p_{1}(1-p_{2})} {p_{2}(1-p_{1})}$$
The conversion to a log odds and its variance is defined as
$$ln(o)= log(or)$$
$$v_{ln(o)}= \frac{1} {A}+ \frac{1} {B}+ \frac{1} {C}+ \frac{1} {D}$$
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.