# Independent Samples T-Test - Equal Variance

Where $\displaystyle{ \bar{x} }$ and $\displaystyle{ \bar{y} }$ are the two means and $\displaystyle{ s_x }$ and $\displaystyle{ s_y }$ respectively are their Standard Deviations, and $\displaystyle{ n_x }$ and $\displaystyle{ n_y }$ are their sample sizes respectively, the test statistic is:
$\displaystyle{ t=\frac{\bar{x}-\bar{y}}{s_\bar{xy}} }$,
$\displaystyle{ p = 2\Pr(t_v \ge |t|) }$,
$\displaystyle{ v = n_x + n_y - 2 }$
$\displaystyle{ s^2_{xy} = ((n_x - 1) s^2_x + (n_y - 1) s^2_y) / v }$, and
$\displaystyle{ s^2_\bar{xy} = s^2_{xy}(n^{-1}_x + n^{-1}_y) }$.