Independent Samples T-Test - Unequal Variance

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

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

where:

$p=2\mathrm{Pr}(t_v\ge |t|)$,

$s_{\overline{i}}^2=\frac{s_i^2}{n_i}$,

$i=x,y$

$v=\frac{(s_{\overline{x}}^2+s_{\overline{y}}^2{)}^2}{\frac{(s_{\overline{x}}^2{)}^2}{n_x-1}+\frac{s_{\overline{y}}^2{)}^2}{n_y-1}}$

$n_i$ is the sample size.