Where \(g_1\) and \(g_2\) are the two proportions and \(n_1\) and \(n_2\) are the sample sizes:
\[\begin{align} z=\frac{g_1-g_2}{\sqrt{d_{eff} \times g_{12}(1-g_{12})\frac{n_1+n_2}{n_1+n_2 - 2b}(n^{-1}_1+n^{-1}_2)}} \end{align}\]
where:
\(g_{12}=\frac{n_1 g_1 + n_2 g_2}{n_1+n_2},\)
\(p = 2(1-\Phi(|z|)),\)
\(b\) is Bessel's correction (see Statistical Assumptions), and
\(d_{eff}\) is Extra Deff (see Weights, Effective Sample Size and Design Effects).