Independent Samples T-Test - Unequal Variance

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

$t={\frac {{\bar {x}}-{\bar {y}}}{\sqrt {s_{\bar {x}}^{2}+s_{\bar {y}}^{2}}}}$,

where:

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

$s_{\bar {i}}^{2}={\frac {s_{i}^{2}}{n_{i}}}$,

$i=x,y$

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

$n_{i}$ is the sample size.