Independent Samples t-Test - Comparing Two Probability %

Where [math]\displaystyle{ \hat{a}_1 }[/math] and [math]\displaystyle{ \hat{a}_1 }[/math] are two probability % and [math]\displaystyle{ n_1 }[/math], [math]\displaystyle{ n_2 }[/math] are their effective sample sizes and [math]\displaystyle{ se_1 }[/math] and [math]\displaystyle{ se_2 }[/math] are their standard errors, the test statistic is:

[math]\displaystyle{ t=\frac{\hat{a}_1-\hat{a}_2}{\sqrt{se^2_1 + se^2_2}} }[/math],

where:

[math]\displaystyle{ p = 2\Pr(t_v \ge |t|) }[/math],

[math]\displaystyle{ v = \frac{(se^2_1+se^2_2)^2}{se^4_1/(n_1-b)+se^4_2/(n_2-b) } }[/math],

[math]\displaystyle{ b = }[/math]Bessel's correction.