A Regression Framework for Rank Tests Based on the Probabilistic Index Model

Abstract

We demonstrate how many classical rank tests, such as the Wilcoxon–Mann–Whitney, Kruskal–Wallis, and Friedman test, can be embedded in a statistical modeling framework and how the method can be used to construct new rank tests. In addition to hypothesis testing, the method allows for estimating effect sizes with an informative interpretation, resulting in a better understanding of the data. Supplementary materials for this article are available online.

• Friedman rank test
• Kruskal–Wallis rank test
• Probabilistic index
• Wilcoxon–Mann–Whitney test.

Additional information

Notes on contributors

Jan De Neve

Jan De Neve is Postdoctoral Researcher at the Department of Mathematical Modelling, Statistics and Bioinformatics of Ghent University, 9000 Gent, Belgium (E-mail: [email protected]). Olivier Thas is Associate Professor at the Department of Mathematical Modelling, Statistics and Bioinformatics of Ghent University, 9000 Gent, Belgium and Honorary Professor at the National Institute for Applied Statistics Research Australia (NIASRA), School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia (E-mail: [email protected]). The authors gratefully acknowledge the Research Fund Flanders (FWO) research grant G020214N and the IAP research network grant no. P7/06 of the Belgian government (Belgian Science Policy).

Olivier Thas

Jan De Neve is Postdoctoral Researcher at the Department of Mathematical Modelling, Statistics and Bioinformatics of Ghent University, 9000 Gent, Belgium (E-mail: [email protected]). Olivier Thas is Associate Professor at the Department of Mathematical Modelling, Statistics and Bioinformatics of Ghent University, 9000 Gent, Belgium and Honorary Professor at the National Institute for Applied Statistics Research Australia (NIASRA), School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia (E-mail: [email protected]). The authors gratefully acknowledge the Research Fund Flanders (FWO) research grant G020214N and the IAP research network grant no. P7/06 of the Belgian government (Belgian Science Policy).