Independent Samples - Quantum Column Proportions Test

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Where p_1 and p_2 are the two proportions and e_1 and e_2 are the effective sample sizes and \pi_1 and \pi_2 are the weighted sample sizes:

t=\frac{p_1-p_2}{\sqrt{p_{12}(1-p_{12})(e^{-1}_1+e^{-1}_2)(\frac{e_1+e_2}{e_1+e_2-1})}}, where p_{12}=\frac{\pi_1 p_1 + \pi_2 p_2}{\pi_1+\pi_2}

where p \approx 2 \Pr(t_{e_1+e_2-1} \ge |t|).

Note that if wishing to replicate results from IBM SPSS Data Collection products (including Survey Reporter and Quantum) additional settings need to be modified (see How to Replicate Survey Reporter Significance Tests).