An algorithm for estimating Box–Cox transformation parameter in ANOVA

ABSTRACT

In this study, we construct a feasible region, in which we maximize the likelihood function, by using Shapiro–Wilk and Bartlett's test statistics to obtain Box–Cox power transformation parameter for solving the issues of non-normality and/or heterogeneity of variances in analysis of variance (ANOVA). Simulation studies illustrate that the proposed approach is more successful in attaining normality and variance stabilization, and is at least as good as the usual maximum likelihood estimation (MLE) in estimating the transformation parameter for different conditions. Our proposed method is illustrated on two real-life datasets. Moreover, the proposed algorithm is released under R package AID under the name of “boxcoxfr” for implementation.

KEYWORDS:

• Data transformation
• Homogeneity test
• Normality test
• Searching algorithms
• Statistical software

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62-07, 62F10
• Secondary 62E17, 62J10

Acknowledgments

The authors thank the anonymous reviewers for their constructive comments and suggestions that helped us to improve the quality of our article.