Independent Samples T-Test - Equal Variance

Where ${\bar {x}}$ and ${\bar {y}}$ are the two means and $s_{x}$ and $s_{y}$ respectively are their Standard Deviations, and $n_{x}$ and $n_{y}$ are their sample sizes respectively, the test statistic is:

$t={\frac {{\bar {x}}-{\bar {y}}}{s_{\bar {xy}}}}$,

where:

$p=2\Pr(t_{v}\geq |t|)$,

$v=n_{x}+n_{y}-2$

$s_{xy}^{2}=((n_{x}-1)s_{x}^{2}+(n_{y}-1)s_{y}^{2})/v$, and

$s_{\bar {xy}}^{2}=s_{xy}^{2}(n_{x}^{-1}+n_{y}^{-1})$.