A Comparison of Tests for Ordered Alternatives With Application in Medicine

Abstract: A situation frequently encountered in medical studies is the comparison of several treatments with a control. The problem is to determine whether or not a test drug has a desirable medical effect and/or to identify the minimum effective dose. In this Bachelor’s thesis, some of the methods used for testing hypotheses of ordered alternatives are reviewed and compared with respect to the power of the tests. Examples of multiple comparison procedures, maximum likelihood procedures, rank tests and different types of contrasts are presented and the properties of the methods are explored. Depending on the degree of knowledge about the dose-responses, the aim of the study, whether the test is parametric or non-parametric and distribution-free or not, different recommendations are given which of the tests should be used. Thus, there is no single test which can be applied in all experimental situations for testing all different alternative hypotheses.