Where \(\bar{x} \) and \(\bar{y} \) are the two means and \(s_x\) and \(s_y\) are their Standard Errors, the test statistic is:
\[\begin{align} t=\frac{\bar{x}-\bar{y}}{\sqrt{s^2_\bar{x} + s^2_\bar{x}}} \end{align},\]
where:
\(p = 2\Pr(t_v \ge |t|)\),
\(v = \frac{(s^2_\bar{x} +s^2_\bar{x})^2}{\frac{(s^2_\bar{x})^2}{n-1}+\frac{s^2_\bar{y})^2}{m-1} }\)
the groups have sample sizes of \(m\) and \(n\) respectively.