Independent Samples T-Test - Equal Variance

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Where [math]\displaystyle{ \bar{x} }[/math] and [math]\displaystyle{ \bar{y} }[/math] are the two means and [math]\displaystyle{ s_x }[/math] and [math]\displaystyle{ s_y }[/math] respectively are their Standard Deviations, and [math]\displaystyle{ n_x }[/math] and [math]\displaystyle{ n_y }[/math] are their sample sizes respectively, the test statistic is:

[math]\displaystyle{ t=\frac{\bar{x}-\bar{y}}{s_\bar{xy}} }[/math],


[math]\displaystyle{ p = 2\Pr(t_v \ge |t|) }[/math],
[math]\displaystyle{ v = n_x + n_y - 2 }[/math]
[math]\displaystyle{ s^2_{xy} = ((n_x - 1) s^2_x + (n_y - 1) s^2_y) / v }[/math], and
[math]\displaystyle{ s^2_\bar{xy} = s^2_{xy}(n^{-1}_x + n^{-1}_y) }[/math].