The Aligned Rank Transform and discrete Variables - a Warning - Kölner UniversitätsPublikationsServer

Lüpsen, Haiko (2017). The Aligned Rank Transform and discrete Variables - a Warning. Communications in Statistics - Simulation and Computation. Taylor & Francis. ISSN 0361-0918 Open Access

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DOI:10.1080/03610918.2016.1217014

Link to the document: http://dx.doi.org/10.1080/03610918.2016.1217014

Abstract

For two-way layouts in a between subjects anova design the aligned rank transform (ART) is compared with the parametric F-test as well as six other nonparametric methods: rank transform (RT), inverse normal transform (INT), a combination of ART and INT, Puri & Sen‘s L statistic, van der Waerden and Akritas & Brunners ATS. The type I error rates are computed for the uniform and the exponential distributions, both as continuous and in several variations as discrete distribution. The computations had been performed for balanced and unbalanced designs as well as for several effect models. The aim of this study is to analyze the impact of discrete distributions on the error rate. And it is shown that this scaling impact is restricted to the ART as well as the combination of ART- and INT-method. There are two effects: first with increasing cell counts their error rates rise beyond any acceptable limit up to 20 percent and more. And secondly their rates rise when the number of distinct values of the dependent variable decreases. This behaviour is more severe for underlying exponential distributions than for uniform distributions. Therefore there is a recommendation not to apply the ART if the mean cell frequencies exceed 10.

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Journal Article

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