lores: Log Odds Ratio to Standardized Mean Difference (d)

Description

Converts a log odds ratio 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

lores(lor, var.lor, n.1, n.2)

Arguments

lor

Log odds ratio reported in the primary study.

var.lor

Variance of the log odds ratio.

n.1

Sample size of treatment group.

n.2

Sample size of comparison group.

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 convert a log odds and its variance to Cohen's $d$. This value will then be used to compute the remaining effect size estimates. One method for deriving 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