CONSEQUENCES OF ASSUMPTION VIOLATIONS REGARDING CLASSICAL LOCATION TESTS

Nearly all classical statistical hypothesis tests are derived under a few fundamental assumptions, which may or may not be met in real world applications. The main aim of this article is to study consequences of a normality assumption violation concerning classical statistical methods, mainly its effect on type I and type II errors when dealing with one-sample or two-sample location tests. The focus will be on a very popular one-sample t-test, as well as on a Behrens-Fisher problem, i.e. on hypothesis testing concerning the difference between expected values of two random variables with unknown and possibly different variances. Based on a simulation study the consequences of different forms of non-normality will be examined for various sample sizes. Type I and type II errors of the classical tests will be then compared with those of appropriate nonparametric tests, specifically with the errors of the Wilcoxon signed-rank and rank-sum tests, as well as the tests based on bootstrap methodology. Based on the results of the conducted simulation study it can be inferred that the classical t-tests tend to be conservative or liberal depending on a form of non-normality. It will be also demonstrated that in case of a contaminated distribution with possible outliers the Wilcoxon tests should be always considered, and that for skewed data and a large sample size the bootstrap BCa method may also be preferable.