Ensemble Based Box-Cox Transformation via Meta Analysis

Abstract

Normal distribution has a vital role for the most of statistical methods. Box-Cox power transformation is the most usually applied method when the distribution of data is not normal. In this study, a novel algorithm is proposed assembling different Box-Cox transformation estimates of the well performed six techniques through random effect model in meta analysis. These techniques include the use of goodness-of-fit tests for normality; Anderson–Darling, Lilliefors, Cramer-von Mises, Shapiro–Wilk, Jarque–Bera and Shapiro–Francia tests. For the estimation of Box-Cox parameter, we assemble all possible combinations (63 combinations) of estimates calculated by these six methods. A Monte-Carlo simulation study is implemented to investigate which combination performs better compared to the rest. The simulation study states that the combination of Shapiro–Wilk, Jarque–Bera and Ander-son–Darling tests performs well in most of the simulation scenarios constructed under different transformation parameters and sample sizes. In this study, this combination is proposed as ensemble based Box-Cox transformation via meta analysis. The proposed approach is implemented on white blood count data of leukaemia patients which are not normally distributed. Also, the proposed methodology is provided in AID R package with “box-coxmeta” function for public use.