Converting Chi-squared ($\chi^2$) statistic with 1 degree of freedom to 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
chies(chi.sq, n)
Arguments
chi.sq
Chi squared statistic from primary study.
n
Sample size in primary study.
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
The chi-squared statistic ($\chi^2$) is defined as
$$\chi^2= \sum{\frac{(o-e)^2} {e}}$$
where $o$ is the observed value and $e$ is the expected value. NOTE: This function requires the $\chi^2$ value to have been derived with 1 degree of freedom (indicating 2 independent groups are used in the calculation).
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.