Independent Complex Samples T-Test - Comparing Two Proportions

Where $g_1$ and $g_2$ are the two proportions, $m$ and $n$ are their sample sizes and $s{e}_1$ and $s{e}_2$ are their standard errors:

$t=\frac{g_1-g_2}{\sqrt{d_{eff}(s{e}_1^2+s{e}_2^2)}}$,

where:

$p=2\mathrm{Pr}(t_v\ge |t|)$,

$v=\frac{(s{e}_1^2+s{e}_2^2{)}^2}{\frac{s{e}_1^4}{n-b}+\frac{s{e}_2^4}{m-b}}$, or, if Weights and significance is set to Un-weighted sample size in tests (see Weights, Effective Sample Size and Design Effects), $v=n+m-2$

$b$ is 1 if Bessel's correction is selected for Proportions in Statistical Assumptions and 0 otherwise.

$d_{eff}$ is Extra Deff.