A distribution-free procedure for testing versatile alternative in medical multisample comparison studies

We propose a test for multisample comparison studies that can be applied without strict assumptions, especially when the underlying population distributions are far from normal. The new test can detect differences not only in location or scale but also in shape parameters among parent population distributions. We are motivated by numerous medical studies, where the variables are not normally distributed and may present in the various groups more complex differences than simple differences in a particular aspect of underlying distributions, such as location or scale. In these situations, traditional ANOVA and Kruskal-Wallis tests are unreliable since the underlying assumptions are not valid. The proposed procedure also allows the researcher to determine which aspects are more responsible for a significant result. This is an important practical advantage over procedures that test for general differences among the distribution functions but cannot identify which aspects lead to significant results. The asymptotic distribution of the test statistic is analyzed along with its small sample behavior against several competing tests. The practical advantages of the proposed procedure are illustrated with a multisample comparison study of a biomarker for liver damage in patients with hepatitis C.