Independent Samples Z-Test - Comparing Two Proportions

Where [math]\displaystyle{ g_1 }[/math] and [math]\displaystyle{ g_2 }[/math] are the two proportions and [math]\displaystyle{ n_1 }[/math] and [math]\displaystyle{ n_2 }[/math] are the sample sizes:

[math]\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^{-1}_2)}} }[/math]

where:

[math]\displaystyle{ g_{12}=\frac{n_1 g_1 + n_2 g_2}{n_1+n_2} }[/math],

[math]\displaystyle{ p = 2(1-\Phi(|z|)) }[/math],

[math]\displaystyle{ b }[/math] is Bessel's correction, and

[math]\displaystyle{ d_{eff} }[/math] is Extra Deff.