A fiducial-based approach to the one-way ANOVA in the presence of nonnormality and heterogeneous error variances

• Published in: Journal of statistical computation and simulation Vol. 89; no. 9; pp. 1715 - 1729
• Main Authors: Güven, Gamze, Gürer, Özge, Şamkar, Hatice, Şenoğlu, Birdal
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 13-06-2019; Taylor & Francis Ltd
• Subjects: Computer simulation; Economic models; Error analysis; fiducial inference; long-tailed symmetric distribution; Maximum likelihood estimators; modified likelihood; Monte Carlo simulation; Normal distribution; Normality; One-way ANOVA; Regression analysis; Statistical tests; Variance analysis
• ISSN: 0094-9655; 1563-5163
• DOI: 10.1080/00949655.2019.1593985

In this study, we propose a new test for testing the equality of the treatment means in one-way ANOVA when the usual normality and the homogeneity of variances assumptions are not met. In developing the proposed test, we benefit from the Fisher's fiducial inference [1-3]. Distribution of the error terms is assumed to be long-tailed symmetric (LTS) which includes the normal distribution as a limiting case. Modified maximum likelihood (MML) estimators are used in the test statistics rather than the traditional least squares (LS) estimators, since LS estimators have very low efficiencies under nonnormal distributions, see Tiku [4] for the details of MML methodology. An extensive Monte Carlo simulation study is done to compare the efficiency of the proposed test with the corresponding test based on normal theory, see Li et al. [5].  Finally, we give a real life example to show the applicability of the proposed methodology.