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

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  • Jan De Neve
  • Olivier Thas

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.

Suggested Citation

  • Jan De Neve & Olivier Thas, 2015. "A Regression Framework for Rank Tests Based on the Probabilistic Index Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1276-1283, September.
    • Handle: RePEc:taf:jnlasa:v:110:y:2015:i:511:p:1276-1283
    DOI: 10.1080/01621459.2015.1016226
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    References listed on IDEAS

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    1. Edgar Brunner & Madan Puri, 2001. "Nonparametric methods in factorial designs," Statistical Papers, Springer, vol. 42(1), pages 1-52, January.
    2. Tsangari, Haritini & Akritas, Michael G., 2004. "Nonparametric ANCOVA with two and three covariates," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 298-319, February.
    3. M. Akritas & A. Stavropoulos & C. Caroni, 2009. "Asymptotic theory of weighted -statistics based on ranks," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(2), pages 177-191.
    4. Olivier Thas & Jan De Neve & Lieven Clement & Jean-Pierre Ottoy, 2012. "Probabilistic index models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(4), pages 623-671, September.
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    1. Amorim, G. & Thas, O. & Vermeulen, K. & Vansteelandt, S. & De Neve, J., 2018. "Small sample inference for probabilistic index models," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 137-148.
    2. Edgar Brunner & Frank Konietschke & Markus Pauly & Madan L. Puri, 2017. "Rank-based procedures in factorial designs: hypotheses about non-parametric treatment effects," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1463-1485, November.
    3. Ejike R. Ugba & Daniel Mörlein & Jan Gertheiss, 2021. "Smoothing in Ordinal Regression: An Application to Sensory Data," Stats, MDPI, vol. 4(3), pages 1-18, July.
    4. Debajit Chatterjee & Uttam Bandyopadhyay, 2019. "Testing in nonparametric ANCOVA model based on ridit reliability functional," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(2), pages 327-364, April.
    5. Dennis Dobler & Sarah Friedrich & Markus Pauly, 2020. "Nonparametric MANOVA in meaningful effects," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(4), pages 997-1022, August.
    6. Haikady N Nagaraja & Shane Sanders, 2020. "The aggregation paradox for statistical rankings and nonparametric tests," PLOS ONE, Public Library of Science, vol. 15(3), pages 1-21, March.

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