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Research Article Open access CC BY 4.0

One-way ANOVA with Bimodal Error Terms

Nuri Celik

Journal of Advances in Mathematics and Computer Science · pp. 168–173 · Published 9 Jul 2023

10.9734/jamcs/2023/v38i81798

Abstract

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.

One-way ANOVA Alpha skew-normal Bimodal data

References (7)

  1. 1 Journal of the American Statistical Association [DOI]
  2. 2 Robustness of the F-Test to Errors of Both Kinds and the Correlation Between the Numerator and Denominator of the F-Ratio [DOI]
  3. 3 Alpha-skew-normal distribution [DOI]
  4. 4 ANALYSIS OF VARIANCE IN EXPERIMENTAL DESIGN WITH NONNORMAL ERROR DISTRIBUTIONS [DOI]
  5. 5 Estimation and Testing in One-Way ANOVA when the Errors are Skew-Normal [DOI]
  6. 6 Robust estimation and testing in one-way ANOVA for Type II censored samples: skew normal error terms [DOI]
  7. 7 Journal of Statistical Computation and Simulation [DOI]

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