One-way ANOVA with Bimodal Error Terms

In this paper, we assume the error distribution of one-way ANOVA as alpha-skew normal distribution. Alpha-skew normal distribution gives us exibility for modelling the data which has heavy tailness, skewness, bimodality and also symmetricity. We obtain the maximum likelihood estimator of the model parameters and the test statistics based on these estimators. Monte Carlo simulation study states that the maximum likelihood estimators of the parameters of interest are more efficient than the corresponding traditional estimators based on normality. Additionally, the test statistics based on maximum likelihood estimators is much more powerful than the test statistics based on traditional normal theory. At the end of this study, a real-life example is made just for illustration of the proposed methodology.