In the two-sample location problem the application of the t-test depends on very restrictive assumptions such as normality and equal variances of the two random variables X and Y. If the assumptions of the t-test are not satisfied it is more appropriate to apply a robust version of the t-test, like the Welch test or the trimmed t-test, or a nonparametric test, like the Wilcoxon. But usually there is no information about the underlying distribution of the data. Therefore, an adaptive test should be applied. Some of these tests are discussed and compared with each other and the classical t-test under different models of nonnormality and for unequal variances. It is shown that an adaptive test behaves well over a broad class of distribution functions.
