Independent Complex Samples T-Test - Comparing Two Proportions

Where $g_{1}$ and $g_{2}$ are the two proportions, $m$ and $n$ are their sample sizes and $s e_{1}$ and $s e_{2}$ are their standard errors:

$t = \frac{g_{1} - g_{2}}{\sqrt{d_{e f f} (s e_{1}^{2} + s e_{2}^{2})}}$ ,

where:

p = 2 \Pr (t_{v} \geq | t |)

,

v = \frac{(s e_{1}^{2} + s e_{2}^{2})^{2}}{\frac{s e_{1}^{4}}{n - b} + \frac{s e_{2}^{4}}{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_{e f f}

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