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

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

$v=n-1$,

$s_{g_{1}-g_{2}}$ 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.