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:

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

where:

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

$s^2_\bar{i} = \frac{s^2_i}{n_i}$,

$i = x, y$

$v = \frac{(s^2_\bar{x} +s^2_\bar{y})^2}{\frac{(s^2_\bar{x})^2}{n_x-1}+\frac{s^2_\bar{y})^2}{n_y-1} }$

$n_i$ is the sample size.