Testing equality of means in one-way ANOVA using three and four moment approximations

Authors : Gamze GUVEN

Pages : 587-605

Doi:10.31801/cfsuasmas.1252070

View : 35 | Download : 58

Publication Date : 2023-09-30

Article Type : Research Paper

Abstract :In this study, we focus on two test statistics for testing the equality of treatment means in one-way analysis of variance insert ignore into journalissuearticles values(ANOVA);. The first one is the well known Cochran insert ignore into journalissuearticles values($C_{LS}$); test statistic based on least squares insert ignore into journalissuearticles values(LS); estimators and the second one is robust version of it insert ignore into journalissuearticles values($RC_{MML}$); based on modified maximum likelihood insert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values(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.
Keywords : Cochran test statistic, three moment chi square approximation, four moment F approximation, Monte Carlo simulation