# Independent Samples Z-Test - Comparing Two Proportions

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

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

where:

${\displaystyle g_{12}={\frac {n_{1}g_{1}+n_{2}g_{2}}{n_{1}+n_{2}}}}$,
${\displaystyle p=2(1-\Phi (|z|))}$,
${\displaystyle b}$ is Bessel's correction, and
${\displaystyle d_{eff}}$ is Extra Deff.