Testing Equality of Multiple Population Means under Contaminated Normal Model Using the Density Power Divergence.

Area of Science:

• Statistics
• Robust Statistics

Background:

• Classical Analysis of Variance (ANOVA) is sensitive to outliers and heavy-tailed error distributions, potentially leading to inaccurate results.
• Data contamination can significantly impact the reliability of treatment effect analysis in ANOVA.

Purpose of the Study:

• To develop a robust statistical test for comparing means in a one-way ANOVA setup.
• To mitigate the adverse effects of outliers and heavy-tailed distributions on ANOVA results.

Main Methods:

• A novel robust ANOVA test is proposed, utilizing an M-estimator derived from the density power divergence.
• Asymptotic properties of the new test were theoretically derived.
• Performance was evaluated through Monte Carlo simulations and analysis of real-world datasets (bone marrow transplant, glucose levels).

Main Results:

• The proposed density power divergence-based M-estimator test demonstrates reduced sensitivity to data contamination compared to existing methods.
• Empirical results show favorable comparisons against classical ANOVA and other robust estimators like Huber's and Tukey's MM-estimators.

Conclusions:

• The proposed robust ANOVA test offers improved analytical performance in the presence of data contamination and non-standard error distributions.
• This method provides a more reliable approach for comparing means in challenging statistical scenarios.