Independent Samples Z-Test - Comparing Two Proportions

Where $g_{1}$ and $g_{2}$ are the two proportions and $n_{1}$ and $n_{2}$ are the sample sizes:

$z={\frac {g_{1}-g_{2}}{\sqrt {d_{eff}\times g_{12}(1-g_{12}){\frac {n_{1}+n_{2}}{n_{1}+n_{2}-2b}}(n_{1}^{-1}+n_{2}^{-1})}}}$

where:

$g_{12}={\frac {n_{1}g_{1}+n_{2}g_{2}}{n_{1}+n_{2}}}$,

$p=2(1-\Phi (|z|))$,

$b$ is Bessel's correction, and

$d_{eff}$ is Extra Deff.