# Independent Samples T-Test - Equal Variance

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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:

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

where:

${\displaystyle p=2\Pr(t_{v}\geq |t|)}$,
${\displaystyle v=n_{x}+n_{y}-2}$
${\displaystyle s_{xy}^{2}=((n_{x}-1)s_{x}^{2}+(n_{y}-1)s_{y}^{2})/v}$, and
${\displaystyle s_{\bar {xy}}^{2}=s_{xy}^{2}(n_{x}^{-1}+n_{y}^{-1})}$.