Dependent Samples - Quantum Column Proportions Test

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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^{-1}_2 - r \frac{2e_o}{e_1 e_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} , and

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).

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

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