Welch's approximation is the most popular solution to the Behrens-Fisher problem, the problem of estimation with small sample sizes with populations of unequal variances, and states that $\frac{\bar X_1 - \bar X_2 - (\mu_1 - \mu_2)}{\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}$ has an approximate [[t-distribution]] with $r$ degrees of freedom where $r = \frac{S^2_1/n_1 + S^2_2/n2}{\frac{(S^2_1/n_1)^2}{n_1-1}+\frac{(S^2_2/n_2)^2}{n_2-1}}$ rounded down.