Independent Samples t-Test - Comparing Two Probability %

Where ${\hat {a}}_{1}$ and ${\hat {a}}_{1}$ are two probability % and $n_{1}$, $n_{2}$ are their effective sample sizes and $se_{1}$ and $se_{2}$ are their standard errors, the test statistic is:

$t={\frac {{\hat {a}}_{1}-{\hat {a}}_{2}}{\sqrt {se_{1}^{2}+se_{2}^{2}}}}$,

where:

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

$v={\frac {(se_{1}^{2}+se_{2}^{2})^{2}}{se_{1}^{4}/(n_{1}-b)+se_{2}^{4}/(n_{2}-b)}}$,

$b=$Bessel's correction.