Two-way ANOVA when the distribution of the error terms is skew t. Issue 1 (2nd January 2019)

• Record Type: Journal Article
• Authors: Celik, Nuri; Senoglu, Birdal
• Is Part Of: Communications in statistics. Volume 48:Issue 1(2019)
• Page Start: 287
• Page End: 301
• Publication Date: 2019-01-02
• Subjects: Iteratively reweighting algorithm -- Modified likelihood -- Monte Carlo simulation -- Skew t distribution -- Two-way ANOVA; 62K25 -- 62F35; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2017.1377242
• Languages: English
• ISSNs: 0361-0918

Abstract

ABSTRACT: In this article, we assume that the distribution of the error terms is skew t in two-way analysis of variance (ANOVA). Skew t distribution is very flexible for modeling the symmetric and the skew datasets, since it reduces to the well-known normal, skew normal, and Student's t distributions. We obtain the estimators of the model parameters by using the maximum likelihood (ML) and the modified maximum likelihood (MML) methodologies. We also propose new test statistics based on these estimators for testing the equality of the treatment and the block means and also the interaction effect. The efficiencies of the ML and the MML estimators and the power values of the test statistics based on them are compared with the corresponding normal theory results via Monte Carlo simulation study. Simulation results show that the proposed methodologies are more preferable. We also show that the test statistics based on the ML estimators are more powerful than the test statistics based on the MML estimators as expected. However, power values of the test statistics based on the MML estimators are very close to the corresponding test statistics based on the ML estimators. At the end of the study, a real life example is given to show the implementation of the proposed methodologies.