Pseudo-Ranks: The Better Way of Ranking?

Georg Zimmermann, Edgar Brunner, Werner Brannath, Martin Happ and Arne C. Bathke

The American Statistician, 2022, vol. 76, issue 2, 124-130

Abstract: Rank-based methods are frequently used in the life sciences, and in the empirical sciences in general. Among the best-known examples of nonparametric rank-based tests are the Wilcoxon-Mann-Whitney test and the Kruskal–Wallis test. However, recently, potential pitfalls and paradoxical results pertaining to the use of traditional rank-based procedures for more than two samples have been highlighted, and the so-called pseudo-ranks have been proposed as a remedy for this type of problems. The aim of the present article is twofold: First, we show that pseudo-ranks might also behave counterintuitively when splitting up groups. Second, since the use of pseudo-ranks leads to a slightly different interpretation of the results, we provide some guidance regarding the decision for one or the other approach, in particular with respect to interpretability and generalizability of the findings. It turns out that the choice of the reference distribution, to which the individual groups are compared, is crucial. The practically relevant implications of these aspects are illustrated by a discussion of a dataset from epilepsy research. Summing up, one should decide based on thorough case-by-case considerations whether ranks or pseudo-ranks are appropriate.

Date: 2022
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DOI: 10.1080/00031305.2021.1972836

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