TESTING EQUALITY OF MEANS IN ONE-WAY ANOVA USING THREE AND FOUR MOMENT APPROXIMATIONS

Guven, Gamze

doi:10.31801/cfsuasmas.1252070

TESTING EQUALITY OF MEANS IN ONE-WAY ANOVA USING THREE AND FOUR MOMENT APPROXIMATIONS

Gamze GUVEN (Eskişehir Osmangazi Üniversitesi, İstatistik Bölümü, 26040, Eskişehir, Türkiye)

Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics

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Yıl: 2023 Cilt: 72 Sayı: 3 Sayfa Aralığı: 587 - 605 Metin Dili: İngilizce DOI: 10.31801/cfsuasmas.1252070 İndeks Tarihi: 06-10-2023

TESTING EQUALITY OF MEANS IN ONE-WAY ANOVA USING THREE AND FOUR MOMENT APPROXIMATIONS

Öz:

In this study, we focus on two test statistics for testing the equality of treatment means in one-way analysis of variance (ANOVA). The first one is the well known Cochran ($C_{LS}$) test statistic based on least squares (LS) estimators and the second one is robust version of it ($RC_{MML}$) based on modified maximum likelihood (MML) estimators. These two test statistics are asymptotically distributed as chi-square. However, distributions of them are unknown for small samples. Therefore, three-moment chi-square and four moment $F$ approximations to the null distributions of $C_{LS}$ and $RC_{MML}$ are derived inspired by Tiku and Wong [19]. To investigate the small and moderate sample properties of these tests based on the mentioned approximations, an extensive Monte-Carlo simulation study is performed when the underlying distribution is long-tailed symmetric (LTS). Simulation results show that four-moment $F$ approximation provides better approximation than the three-moment chi-square approximation for both $C_{LS}$ and $RC_{MML}$ tests. Therefore, the simulated Type I error rates and powers of the $C_{LS}$ and $RC_{MML}$ test statistics are calculated using four-moment $F$ approximation. According to simulation results, $RC_{MML}$ test is more powerful than the corresponding $C_{LS}$ test.

Anahtar Kelime: Cochran test statistic three moment chi-square approximation four-moment F approximation Monte Carlo simulation

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

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APA	Guven G (2023). TESTING EQUALITY OF MEANS IN ONE-WAY ANOVA USING THREE AND FOUR MOMENT APPROXIMATIONS. , 587 - 605. 10.31801/cfsuasmas.1252070
Chicago	Guven Gamze TESTING EQUALITY OF MEANS IN ONE-WAY ANOVA USING THREE AND FOUR MOMENT APPROXIMATIONS. (2023): 587 - 605. 10.31801/cfsuasmas.1252070
MLA	Guven Gamze TESTING EQUALITY OF MEANS IN ONE-WAY ANOVA USING THREE AND FOUR MOMENT APPROXIMATIONS. , 2023, ss.587 - 605. 10.31801/cfsuasmas.1252070
AMA	Guven G TESTING EQUALITY OF MEANS IN ONE-WAY ANOVA USING THREE AND FOUR MOMENT APPROXIMATIONS. . 2023; 587 - 605. 10.31801/cfsuasmas.1252070
Vancouver	Guven G TESTING EQUALITY OF MEANS IN ONE-WAY ANOVA USING THREE AND FOUR MOMENT APPROXIMATIONS. . 2023; 587 - 605. 10.31801/cfsuasmas.1252070
IEEE	Guven G "TESTING EQUALITY OF MEANS IN ONE-WAY ANOVA USING THREE AND FOUR MOMENT APPROXIMATIONS." , ss.587 - 605, 2023. 10.31801/cfsuasmas.1252070
ISNAD	Guven, Gamze. "TESTING EQUALITY OF MEANS IN ONE-WAY ANOVA USING THREE AND FOUR MOMENT APPROXIMATIONS". (2023), 587-605. https://doi.org/10.31801/cfsuasmas.1252070

APA	Guven G (2023). TESTING EQUALITY OF MEANS IN ONE-WAY ANOVA USING THREE AND FOUR MOMENT APPROXIMATIONS. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 72(3), 587 - 605. 10.31801/cfsuasmas.1252070
Chicago	Guven Gamze TESTING EQUALITY OF MEANS IN ONE-WAY ANOVA USING THREE AND FOUR MOMENT APPROXIMATIONS. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 72, no.3 (2023): 587 - 605. 10.31801/cfsuasmas.1252070
MLA	Guven Gamze TESTING EQUALITY OF MEANS IN ONE-WAY ANOVA USING THREE AND FOUR MOMENT APPROXIMATIONS. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, vol.72, no.3, 2023, ss.587 - 605. 10.31801/cfsuasmas.1252070
AMA	Guven G TESTING EQUALITY OF MEANS IN ONE-WAY ANOVA USING THREE AND FOUR MOMENT APPROXIMATIONS. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics. 2023; 72(3): 587 - 605. 10.31801/cfsuasmas.1252070
Vancouver	Guven G TESTING EQUALITY OF MEANS IN ONE-WAY ANOVA USING THREE AND FOUR MOMENT APPROXIMATIONS. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics. 2023; 72(3): 587 - 605. 10.31801/cfsuasmas.1252070
IEEE	Guven G "TESTING EQUALITY OF MEANS IN ONE-WAY ANOVA USING THREE AND FOUR MOMENT APPROXIMATIONS." Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 72, ss.587 - 605, 2023. 10.31801/cfsuasmas.1252070
ISNAD	Guven, Gamze. "TESTING EQUALITY OF MEANS IN ONE-WAY ANOVA USING THREE AND FOUR MOMENT APPROXIMATIONS". Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 72/3 (2023), 587-605. https://doi.org/10.31801/cfsuasmas.1252070