Independent Complex Samples T-Test - Comparing Two Proportions

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Where g_1 and g_2 are the two proportions, m and n are their sample sizes and se_1 and se_2 are their standard errors:

t=\frac{g_1-g_2}{\sqrt{d_{eff}(se^2_1 + se^2_2)}},

where:

p = 2\Pr(t_v \ge |t|),
v = \frac{(\frac{se^2_1}{n} +\frac{se^2_2}{m} )^2}{\frac{(\frac{se^2_1}{n})^2}{n-b}+\frac{(\frac{se^2_2}{m})^2}{m-b} } , or, if Weights and significance is set to Un-weighted sample size in tests (see Weights, Effective Sample Size and Design Effects), v = n + m - 2
b is 1 if Bessel's correction is selected for Proportions in Statistical Assumptions and 0 otherwise.
d_{eff} is Extra Deff.
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