Dependent Samples - Survey Reporter Column Proportions Test

Where $p_1$ and $p_2$ are the two proportions, $e_1$ and $e_2$ are the effective sample sizes, ${\pi }_1$ and ${\pi }_2$ are the weighted sample sizes, $r$ is Pearson's Product Moment Correlation for the overlapping sample and $e_o$ is the effective sample size that overlaps between the two samples, the test statistic is:

$t=\frac{p_1-p_2}{\sqrt{p_{12}(1-p_{12})(e_1^{-1}+e_2^{-1}-r\frac{2e_o}{e_1{e}_2}})}$,

where:

$p_{12}=\frac{{\pi }_1{p}_1+{\pi }_2{p}_2}{{\pi }_1+{\pi }_2}$, and

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

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).

Also note that if $e_o=0$ the Independent version of the test is conducted instead.