On the proper use of Box-Cox transformation method: a note on a Taguchi case study

• Main Author: YANG, Zhenlin
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2000
• Subjects: Box-cox transformation; heteroscedasticity; noise performance measure; target performance measure; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/2069; https://ink.library.smu.edu.sg/context/soe_research/article/3068/viewcontent/Yang_BCTaguchi00.pdf
• Institution: Singapore Management University

In studying the role of transformation in the Taguchi method, Logothetis (1990) analyzed the data from a plasma etching process and concluded that the Box-Cox method can induce a mean bias in the variability performance measure which can inhibit the production of clearcut results. This paper points out that the above conclusion is in part due to an inappmpriate application of the Box-Cox method where the transformation parameter is determined from one model but the analysis is done on the other. Further, it may not be appropriate to state that Box-Cox method induces a mean bias, but rather that there exists an intrinsic nonlinear relationship between the trial means and the trial Variances and the Box-Cox transformation applied to the original data is just unable to transform it away. However, if the Box-Cox transformation is applied to the original trial means and standard deviations, the dependence vanishes and clearcut results are obtained.