Where \(g_1\) and \(g_2\) are the two proportions and \(n_1\) and \(n_2\) are the sample sizes:
\[\begin{align} z=\frac{g_1-g_2}{\sqrt{g_{12}(1-g_{12})(n^{-1}_1+n^{-1}_2)}} \end{align}\]
where:
\[\begin{align} g_{12}=\frac{n_1 g_1 + n_2 g_2}{n_1+n_2} \end{align}\]
where \(p \approx 2 \Pr(t_{n_1+n_2-2} \ge |t|)\).