Paired t-Test of Proportions

Where $g_1$ and $g_2$ are the two proportions, $n$ is the sample size, and $s_{g_1-g_2}$ is an estimate of the standard error of the difference between the proportions:

$t=\frac{g_1-g_2}{s_{g_1-g_2}}$

where

$p=2\mathrm{Pr}(t_v\ge |t|)$,

$v=n-1$,

$s_{g_1-g_2}$ is computed as the Standard Error of $d$,

the value for the $i$th observation is computed as $d_i=x_1-x_2$,

$x_1,x_2\in \{0,1\}$ are the observed values on the two variables.