- Hacettepe Journal of Mathematics and Statistics
- Vol: 51 Issue: 6
- Testing the equality of treatment means in one-way ANOVA: Short-tailed symmetric error terms with he...
Testing the equality of treatment means in one-way ANOVA: Short-tailed symmetric error terms with heterogeneous variances
Authors : Gamze Guven
Pages : 1736-1751
Doi:10.15672/hujms.1055277
View : 11 | Download : 3
Publication Date : 2022-12-01
Article Type : Research
Abstract :We propose two tests based on fiducial and generalized $p$-value approaches for testing the equality of treatment means in one-way analysis of variance (ANOVA). Modified maximum likelihood (MML) estimators are used in the proposed tests. In contrast to least squares (LS) estimators, MML estimators are highly efficient and robust to plausible deviations from an assumed distribution and to mild data anomalies. In this study, error terms are assumed to have short-tailed symmetric (STS) distributions with heterogeneous variances. The performances of the proposed tests are compared with the fiducial based test using bias-corrected LS estimators via an extensive Monte Carlo simulation study. Finally, two real datasets are analyzed for illustrative purposes.Keywords : One-way ANOVA, short tailed symmetric distribution, fiducial based test, generalized F test, modified maximum likelihood, Monte Carlo simulation