# Independent Samples T-Test - Unequal Variance

Where ${\displaystyle {\bar {x}}}$ and ${\displaystyle {\bar {y}}}$ are the two means and ${\displaystyle s_{x}}$ and ${\displaystyle s_{y}}$ are their Standard Deviations, the test statistic is:
${\displaystyle t={\frac {{\bar {x}}-{\bar {y}}}{\sqrt {s_{\bar {x}}^{2}+s_{\bar {y}}^{2}}}}}$,
${\displaystyle p=2\Pr(t_{v}\geq |t|)}$,
${\displaystyle s_{\bar {i}}^{2}={\frac {s_{i}^{2}}{n_{i}}}}$,
${\displaystyle i=x,y}$
${\displaystyle v={\frac {(s_{\bar {x}}^{2}+s_{\bar {y}}^{2})^{2}}{{\frac {(s_{\bar {x}}^{2})^{2}}{n_{x}-1}}+{\frac {s_{\bar {y}}^{2})^{2}}{n_{y}-1}}}}}$
${\displaystyle n_{i}}$ is the sample size.