The test statistic is:
\[\begin{align} t = \frac{\bar{x} - \bar{y}}{\sqrt{\frac{s^2_x}{m} + \frac{s^2_y}{n}}} \end{align}\]
where:
\(\bar{x} \) and \(\bar{y} \) are the average values of variables \(x\) and \(y\) respectively where each of these variables represents the data from two independent groups, the groups have sample sizes of \(m\) and \(n\) respectively,
\(s^2_x\) and \(s^2_y\) are the variances in the two groups,
\(p = 2\Pr(t_v \ge |t|),\)
\(v = \frac{(\frac{s^2_x}{n} +\frac{s^2_y}{m} )^2}{\frac{(\frac{s^2_x}{n / d_{eff}})^2}{n-b}+\frac{(\frac{s^2_y}{m / d_{eff}})^2}{m-b} },\)
\(b\) is if Bessel's correction is selected for Means in Statistical Assumptions and 0 otherwise,
\(d_{eff} \) is Extra Deff (see Weights, Effective Sample Size and Design Effects).