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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2010 / Cilt: 59 - Sayı: 2

A SIMULATION STUDY ON TESTS FOR ONE-WAY ANOVA UNDER THE UNEQUAL VARIANCE ASSUMPTION

Esra YİĞİT
Fikri GÖKPINAR
Pages
15–34
Publication Date
2010-08-01
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In this study, the Brown-Forsythe, Weerahandiís Generalized F, Parametric Bootstrap, Scott-Smith, One-Stage, One-Stage Range, Welch and Xu-Wangís Generalized F-tests are introduced and a simulation study is performed to compare these tests according to type-1 errors and powers in different combinations of parameters and various sample sizes.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The classical F-test to compare several population means depends on the assumption of homogeneity of variance of the population and the normality.
📊
Key Findings & Data:When these assumptions especially the equality of variance is dropped, the classical F-test fails to reject the null hypothesis even if the data actually provide strong evidence for it.
💡
Conclusion & Impact:In this study, the Brown-Forsythe, Weerahandiís Generalized F, Parametric Bootstrap, Scott-Smith, One-Stage, One-Stage Range, Welch and Xu-Wangís Generalized F-tests are introduced and a simulation study is performed to compare these tests according to type-1 errors and powers in different combinations of parameters and various sample sizes.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Brown-Forsythe test · Generalized F-test · Parametric Bootstrap test

Abstract

The classical F-test to compare several population means depends on the assumption of homogeneity of variance of the population and the normality. When these assumptions especially the equality of variance is dropped, the classical F-test fails to reject the null hypothesis even if the data actually provide strong evidence for it. This can be considered a serious problem in some applications, especially when the sample size is not large. To deal with this problem, a number of tests are available in the literature. In this study, the Brown-Forsythe, Weerahandiís Generalized F, Parametric Bootstrap, Scott-Smith, One-Stage, One-Stage Range, Welch and Xu-Wangís Generalized F-tests are introduced and a simulation study is performed to compare these tests according to type-1 errors and powers in different combinations of parameters and various sample sizes.

🔖

Cite This Article

YİĞİT, E., GÖKPINAR, F. (2010). A SIMULATION STUDY ON TESTS FOR ONE-WAY ANOVA UNDER THE UNEQUAL VARIANCE ASSUMPTION. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Cilt: 59 - Sayı: 2, 15–34. https://ajindex.com/articles/747444

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