The Effects of the Box–Cox Transformation

Abstract

The expected effects of the Box–Cox transformation (BCT), when applied to available data, have been summarized in the original article, where the transformation was first introduced. It was to achieve validity for the three major assumptions made in the analysis of linear models, that is, simplicity of structure (of the linear model), constancy of error variance, and normality of distributions. While many articles have been published to date about estimating the parameter(s) of BCT, or suggesting alternatives, little attention has been given to the more fundamental question – Why should a data power transformation be able to achieve these objectives (as cumulative empirical evidence obviously attest to)? In this article, we address this question and attempt clear explanation with regard to each of the objectives that BCT attempts to achieve.