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Journals / The European Research Journal / 2026 / Volume: 9 Issue: 1

Comparison of the performances of parametric k-sample test procedures as an alternative to one-way analysis of variance

Gökhan Ocakoğlu(Department of Biostatistics, Bursa Uludağ University, Faculty of Medicine, Bursa, Turkey)0000-0002-1114-6051
Aslı Ceren Macunluoglu(Department of Biostatistics, Bursa Uludağ University, Institute of Health Sciences, Bursa, Turkey)0000-0002-6802-5998
Pages
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Publication Date
2023-01-04
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AI Summary & Key Takeaways

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

Conclusions: The Welch test, the Alexander-Govern test and the James Second-Order test are the tests that can be recommended as an alternative to the F test.

📌 3 Key Takeaways

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Objective & Hypothesis:Objectives: The performances of the Welch test, the Alexander-Govern test, the Brown-Forsythe test and the James Second-Order test, which are among the parametric alternatives of one-way analysis of variance and included in the literature, to protect the Type-I error probability determined at the beginning of the trial at a nominal level, were compared with the F test.
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Key Findings & Data:Methods: Performance of the tests to protect Type-I error; in cases where the variances are homogeneous and heterogeneous, the sample sizes are balanced and unbalanced, the distribution of the data is in accordance with the normal distribution and the log-normal distribution, how it is affected by the change in the number of groups to be compared has been examined on simulation scenarios.
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Conclusion & Impact:Conclusions: The Welch test, the Alexander-Govern test and the James Second-Order test are the tests that can be recommended as an alternative to the F test.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Analysis of variance · conformity of normal distribution · parametric k-sample tests

Abstract

Objectives: The performances of the Welch test, the Alexander-Govern test, the Brown-Forsythe test and the James Second-Order test, which are among the parametric alternatives of one-way analysis of variance and included in the literature, to protect the Type-I error probability determined at the beginning of the trial at a nominal level, were compared with the F test. Methods: Performance of the tests to protect Type-I error; in cases where the variances are homogeneous and heterogeneous, the sample sizes are balanced and unbalanced, the distribution of the data is in accordance with the normal distribution and the log-normal distribution, how it is affected by the change in the number of groups to be compared has been examined on simulation scenarios. Results: The Welch test, the Alexander-Govern test and the James Second-Order test were not affected by the distribution and performed well in situations where variances were heterogeneous. The Brown-Forsythe test was not affected by the distribution, it performed well when the variance was homogeneous and the sample size in the groups to be compared was not equal. Conclusions: The Welch test, the Alexander-Govern test and the James Second-Order test are the tests that can be recommended as an alternative to the F test.

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Cite This Article

Ocakoğlu, G., Macunluoglu, A. C. (2023). Comparison of the performances of parametric k-sample test procedures as an alternative to one-way analysis of variance. The European Research Journal, Volume: 9 Issue: 1. https://doi.org/10.18621/eurj.1030038

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