# Independent Samples t-Test - Comparing Two Probability %

Where $\displaystyle{ \hat{a}_1 }$ and $\displaystyle{ \hat{a}_1 }$ are two probability % and $\displaystyle{ n_1 }$, $\displaystyle{ n_2 }$ are their effective sample sizes and $\displaystyle{ se_1 }$ and $\displaystyle{ se_2 }$ are their standard errors, the test statistic is:
$\displaystyle{ t=\frac{\hat{a}_1-\hat{a}_2}{\sqrt{se^2_1 + se^2_2}} }$,
$\displaystyle{ p = 2\Pr(t_v \ge |t|) }$,
$\displaystyle{ v = \frac{(se^2_1+se^2_2)^2}{se^4_1/(n_1-b)+se^4_2/(n_2-b) } }$,
$\displaystyle{ b = }$Bessel's correction.