T-Test of Two Mutually Exclusive Proportions

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Where [math]\displaystyle{ g_1 }[/math] and [math]\displaystyle{ g_2 }[/math] are the two proportions:

[math]\displaystyle{ t=\frac{g_1-g_2}{\sqrt{d_{eff}(\frac{g_1+g_2 - (g_1-g_2)^2)}{n - 1})}} }[/math]


[math]\displaystyle{ p \approx 2\Pr(t_{n-1} \ge |t|) }[/math],
[math]\displaystyle{ b }[/math] is 1 if Bessel's correction for Means is selected in Statistical Assumptions and 0 otherwise,
[math]\displaystyle{ d_{eff} }[/math] is Extra deff, and
[math]\displaystyle{ n }[/math] is the unweighted sample size.