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:

$g_{12}=\frac{n_1{g}_1+n_2{g}_2}{n_1+n_2}$,

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

$b$ is Bessel's correction, and

$d_{eff}$ is Extra Deff.