ON NONPARAMETRIC AND GENERALIZED TESTS FOR THE 2-SAMPLE PROBLEM WITH LOCATION AND SCALE CHANGE ALTERNATIVES

Various tests have been proposed for the two-sample problem when the a lternative is more general than a simple shift in location: non-parame tric tests; O'Brien's generalized t and rank sum tests; and other test s related to the t. We show that the generalized tests are directly re lated to non-parametric tests proposed by Lepage. As a result, we obta in a wider, more flexible class of O'Brien-type procedures which inher it the level robustness property of non-parametric tests. We have also computed the tests' empirical sizes and powers under several models. The non-parametric procedures and the related O'Brien-type tests are v alid and yield good power in the settings investigated. They are prefe rable to the t-test and related procedures whose type I errors differ noticeably from nominal size for skewed and long-tailed distributions.