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Title: The impact of sample non-normality on ANOVA and alternative methods
Authors: Lantz, Björn
Department: University of Borås. School of Engineering
Issue Date: 2013
Journal Title: British Journal of Mathematical and Statistical Psychology
ISSN: 2044-8317
Volume: 66
Issue: 2
Pages: 224-244
Publisher: John Wiley & Sons Ltd.
Media type: text
Publication type: article, peer reviewed scientific
Subject Category: Subject categories::Mathematics
Area of Research: IH Logistik/Logistics
Strategic Research Area: none
Abstract: In this journal, Zimmerman (2004, 2011) has discussed preliminary tests that researchers often use to choose an appropriate method for comparing locations when the assumption of normality is doubtful. The conceptual problem with this approach is that such a two-stage process makes both the power and the significance of the entire procedure uncertain, as type I and type II errors are possible at both stages. A type I error at the first stage, for example, will obviously increase the probability of a type II error at the second stage. Based on the idea of Schmider et al. (2010), which proposes that simulated sets of sample data be ranked with respect to their degree of normality, this paper investigates the relationship between population non-normality and sample non-normality with respect to the performance of the ANOVA, Brown–Forsythe test, Welch test, and Kruskal–Wallis test when used with different distributions, sample sizes, and effect sizes. The overall conclusion is that the Kruskal–Wallis test is considerably less sensitive to the degree of sample normality when populations are distinctly non-normal and should therefore be the primary tool used to compare locations when it is known that populations are not at least approximately normal.
DOI: 10.1111/j.2044-8317.2012.02047.x
URI: http://hdl.handle.net/2320/11512
Sustainable development: -
Appears in Collections:Artiklar och rapporter / Articles and reports (IH)

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