Nonparametric Two-Sample Tests in Case of Heteroscedasticity

Heteroscedasticity and non-normal data are both very common in various applications. In this case, nonparametric location-scale tests and/or
tests for the nonparametric Behrens-Fisher problem can be appropriate. Because the hypotheses for these two approaches differ, it is discussed which hypothesis is justified in which situation. Moreover, an overview of available tests for the two-sample problem is given. Classical nonparametric tests as well as novel and little-known methods are included. Simulation results are presented in order to compare the different tests. A special focus is given to non-continuous distributions as ties frequently occur in practice. Examples and computational issues are also mentioned.