Single-stage analysis of variance under heteroscedasticity

Chen, Shun-Yi; Chen, Hubert J.

doi:10.1080/03610919808813501

Cited by 29 publications

(11 citation statements)

References 2 publications

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“…which is a quadratic form in the independent student's t variates each with n 0 -1 degrees of freedom (Chen and Chen, 1998). For a given level , and an observed valueF 1 h ofF 1 , this test rejects the H 0 in (2.1) whenever the p-value is given as…”

Section: The One-stage Testmentioning

confidence: 99%

“…Some of these test statistics'distribution is not known and the p-value can be found by simulation (Weerahandi, 1995;Weerahandi, 2004). There are a large number of approximate tests (Chen and Chen, 1998;Chen, 2001; Tsui and Weerahandi, 1989; Krishnamoorthy et al, 2006;Wang, 2007a, 2007b) and exact tests (Bishop and Dudewicz, 1981;Welch, 1951;Scott and Smith, 1971; Brown and Forsythe, 1974) in the literature. In practice, some exact procedures such as the CF, Welch (W), Scott-Smith (SS) and Brown-Forsythe (BF) tests are widely used.…”

Section: Introductionmentioning

confidence: 99%

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A Simulation Study on Tests for One-Way Anova Under the Unequal Variance Assumption

Yiğit¹,

Gökpinar²

2010

Communications, Faculty of Science, University of Ankara Series A1Mathematics and Statistics

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C o m m u n .Fa c .S c i.U n iv .A n k .S e rie s A 1 Vo lu m e 5 9 , N u m b e r 2 , P a g e s 1 5 -3 4 (2 0 1 0 ) IS S N 1 3 0 3 -5 9 9 1 A SIMULATION STUDY ON TESTS FOR ONE-WAY ANOVA UNDER THE UNEQUAL VARIANCE ASSUMPTION ESRA YI ¼ GIT AND FIKRI GÖKPINARAbstract. 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, Weerahandi's Generalized F, Parametric Bootstrap, Scott-Smith, One-Stage, One-Stage Range, Welch and Xu-Wang's Generalized F-tests are introduced and a simulation study is performed to compare these tests according to type-1 errors and powers in di¤erent combinations of parameters and various sample sizes.

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Section: The One-stage Testmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Simulation Study on Tests for One-Way Anova Under the Unequal Variance Assumption

Yiğit¹,

Gökpinar²

2010

Communications, Faculty of Science, University of Ankara Series A1Mathematics and Statistics

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“…It was proved that the conditional normal distributions of t i are unconditional and independent Student's t distributions with n i 2 degrees of freedom [2]. In other words, the joint p.d.f.…”

Section: The Single-stage Testmentioning

confidence: 99%

“…The two-stage test suggested by Dudewicz and Dalal [6] was applied on variance analysis problems by Bishop and Dudewicz [7]. Chen and Chen compared the single-stage test with the two-stage test to test the null hypothesis about the equality of means [2].…”

Section: Introductionmentioning

confidence: 99%

On the Comparison of the Welch Test and the Single-Stage Test a Simulation Study

Ekiz¹,

Gamgam²

1999

Communications, Faculty of Science, University of Ankara Series A1Mathematics and Statistics

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“….., k, have independent Student's t-distributions, free of the unknown variances σ 2 i (see, e.g., Chen and Chen (1998)). …”

Section: Two-stage Procedures and Modified Studentized Range Testmentioning

confidence: 99%

A studentized range test for the equivalency of normal means under heteroscedasticity

Wen

Chen

2006

Computational Statistics & Data Analysis

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Single-stage analysis of variance under heteroscedasticity

Cited by 29 publications

References 2 publications

A Simulation Study on Tests for One-Way Anova Under the Unequal Variance Assumption

A Simulation Study on Tests for One-Way Anova Under the Unequal Variance Assumption

On the Comparison of the Welch Test and the Single-Stage Test a Simulation Study

A studentized range test for the equivalency of normal means under heteroscedasticity

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