# Independent Samples - Survey Reporter Column Proportions Test

Where ${\displaystyle p_{1}}$ and ${\displaystyle p_{2}}$ are the two proportions, ${\displaystyle e_{1}}$ and ${\displaystyle e_{2}}$ are the effective sample sizes and ${\displaystyle \pi _{1}}$ and ${\displaystyle \pi _{2}}$ are the weighted sample sizes:
${\displaystyle t={\frac {p_{1}-p_{2}}{\sqrt {p_{12}(1-p_{12})(e_{1}^{-1}+e_{2}^{-1})}}}}$, where ${\displaystyle p_{12}={\frac {\pi _{1}p_{1}+\pi _{2}p_{2}}{\pi _{1}+\pi _{2}}}}$
where ${\displaystyle p\approx 2\Pr(t_{e_{1}+e_{2}-2}\geq |t|)}$.