Independent Complex Samples T-Test - Comparing Two Proportions

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Where [math]\displaystyle{ g_1 }[/math] and [math]\displaystyle{ g_2 }[/math] are the two proportions, [math]\displaystyle{ m }[/math] and [math]\displaystyle{ n }[/math] are their sample sizes and [math]\displaystyle{ se_1 }[/math] and [math]\displaystyle{ se_2 }[/math] are their standard errors:

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


[math]\displaystyle{ p = 2\Pr(t_v \ge |t|) }[/math],
[math]\displaystyle{ v = \frac{(se^2_1 +se^2_2)^2}{\frac{se^4_1}{n-b}+\frac{se^4_2}{m-b} } }[/math], or, if Weights and significance is set to Un-weighted sample size in tests (see Weights, Effective Sample Size and Design Effects), [math]\displaystyle{ v = n + m - 2 }[/math]
[math]\displaystyle{ b }[/math] is 1 if Bessel's correction is selected for Proportions in Statistical Assumptions and 0 otherwise.
[math]\displaystyle{ d_{eff} }[/math] is Extra Deff.