Independent Complex Samples T-Test - Comparing Two Proportions

Where ${\displaystyle g_{1}}$ and ${\displaystyle g_{2}}$ are the two proportions, ${\displaystyle m}$ and ${\displaystyle n}$ are their sample sizes and ${\displaystyle se_{1}}$ and ${\displaystyle se_{2}}$ are their standard errors:
${\displaystyle t={\frac {g_{1}-g_{2}}{\sqrt {d_{eff}(se_{1}^{2}+se_{2}^{2})}}}}$,
${\displaystyle p=2\Pr(t_{v}\geq |t|)}$,
${\displaystyle v={\frac {({\frac {se_{1}^{2}}{n}}+{\frac {se_{2}^{2}}{m}})^{2}}{{\frac {({\frac {se_{1}^{2}}{n}})^{2}}{n-b}}+{\frac {({\frac {se_{2}^{2}}{m}})^{2}}{m-b}}}}}$, or, if Weights and significance is set to Un-weighted sample size in tests (see Weights, Effective Sample Size and Design Effects), ${\displaystyle v=n+m-2}$
${\displaystyle b}$ is 1 if Bessel's correction is selected for Proportions in Statistical Assumptions and 0 otherwise.
${\displaystyle d_{eff}}$ is Extra Deff.