Where \(\bar{x}\) and \(\bar{y}\) are the two means, and \(s_\bar{x}\) and \(s_\bar{y}\) are their Standard Errors, the test statistic is:
\[\begin{align} t=\frac{\bar{x}-\bar{y}}{\sqrt{s^2_\bar{x} + s^2_\bar{y}}} \end{align},\]
where:
\(p = 2\Pr(t_v \ge |t|),\)
\(v = \frac{(s^2_\bar{x} +s^2_\bar{y})^2}{\frac{s^4_\bar{x}}{n-b}+\frac{s^4_\bar{y}}{m-b} }\)
the groups have sample sizes of \(m\) and \(n\) respectively (or effective sample sizes if a design effect has been specified),
\(b\) is 1 if Bessel's correction is selected for Means in Statistical Assumptions and 0 otherwise.