Independent Samples T-Test - Pooled Variance

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Where [math]\displaystyle{ \bar{x}_i }[/math] is the mean of variable [math]\displaystyle{ x }[/math] for the [math]\displaystyle{ i }[/math]th of [math]\displaystyle{ g }[/math] groups, [math]\displaystyle{ s_{x_i} }[/math] is its Standard Deviation and [math]\displaystyle{ n_i }[/math] its sample size, the test statistic is for the difference between groups [math]\displaystyle{ i }[/math] and [math]\displaystyle{ i' }[/math] is given by:

[math]\displaystyle{ t=\frac{\bar{x}_i-\bar{x}_{i'}}{\sqrt{s^2_x(n^{-1}_i + n^{-1}_{i'})}} }[/math],


[math]\displaystyle{ p = 2\Pr(t_v \ge |t|) }[/math],
[math]\displaystyle{ v = \sum^g_{i=1} n_i - g }[/math], and
[math]\displaystyle{ s^2_{x} = \sum^g_{i=1}{ ( n_i - 1 ) s^2_{x_i}} / v }[/math].