Universität zu Köln

Lüpsen, Haiko (2017). Comparison of nonparametric analysis of variance methods - A Vote for van der Waerden. Communications in Statistics - Simulation and Computation, 30. pp. 1-30. Taylor & Francis.

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Abstract

For two-way layouts in a between subjects anova design the parametric F-test is compared with seven nonparametric methods: rank transform (RT), inverse normal transform (INT), aligned rank transform (ART), a combination of ART and INT, Puri & Sen‘s L statistic, van der Waerden and Akritas & Brunners ATS. The type I error rates and the power are computed for 16 normal and nonnormal distributions, with and without homogeneity of variances, for balanced and unbalanced designs as well as for several models including the null and the full model. The aim of this study is to identify a method that is applicable without too much testing all the attributes of the plot. The van der Waerden-test shows the overall best performance though there are some situations in which it is disappointing. The Puri & Sen- and the ATS-tests show generally a very low power. These two as well as the other methods cannot keep the type I error rate under control in too many situations. Especially in the case of lognormal distributions the use of any of the rank based procedures can be dangerous for cell sizes above 10. As already shown by many other authors, nonnormal distributions do not violate the parametric F-test, but unequal variances do. And heterogeneity of variances leads to an inflated error rate more or less also for the nonparametric methods. Finally it should be noted that some procedures show rising error rates with increasing cell sizes, the ART, especially for discrete variables, as well as the RT, Puri & Sen and the ATS in the cases of heteroscedasticity.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Lüpsen, Haiko luepsen@uni-koeln.de UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-85439
DOI:	10.1080/03610918.2017.1353613
Journal or Publication Title:	Communications in Statistics - Simulation and Computation
Volume:	30
Page Range:	pp. 1-30
Date:	2017
Publisher:	Taylor & Francis
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Institute of Computer Science
Subjects:	General statistics
Uncontrolled Keywords:	Keywords Language nonparametric anova, rank transform, Puri & Sen, ATS, Waerden, simulation English
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/8543