A closer examination on some parametric alternatives to the ANOVA Ftest
 A. De Beuckelaer
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In experiments, the classical (ANOVA) Ftest is often used to test the omnibus nullhypothesis μ_{1} = μ_{2} ... = μ_{ j } = ... = μ_{ n } (all n population means are equal) in a oneway ANOVA design, even when one or more basic assumptions are being violated. In the first part of this article, we will briefly discuss the consequences of the different types of violations of the basic assumptions (dependent measurements, nonnormality, heteroscedasticity) on the validity of the Ftest. Secondly, we will present a simulation experiment, designed to compare the type Ierror and power properties of both the Ftest and some of its parametric adaptations: the Brown & Forsythe F^{*}test and Welch’s V_{w}test. It is concluded that the Welch V_{w}test offers acceptable control over the type Ierror rate in combination with (very) high power in most of the experimental conditions. Therefore, its use is highly recommended when one or more basic assumptions are being violated. In general, the use of the Brown & Forsythe F^{*}test cannot be recommended on power considerations unless the design is balanced and the homoscedasticity assumption holds.
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 Title
 A closer examination on some parametric alternatives to the ANOVA Ftest
 Journal

Statistical Papers
Volume 37, Issue 4 , pp 291305
 Cover Date
 19961201
 DOI
 10.1007/BF02926110
 Print ISSN
 09325026
 Online ISSN
 16139798
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 robust analysis of variance (ANOVA)
 oneway ANOVA design
 Brown & Forsythe F*(test)
 Welch Vw(test)
 Monte Carlo simulation
 Industry Sectors
 Authors

 A. De Beuckelaer ^{(1)}
 Author Affiliations

 1. Faculty of Applied Economics Computer Science and Operations Management, University of AntwerpRUCA, Middelheimlaan 1, B2020, Antwerpen, Belgium