EVALUATION OF JOHNSON’S SYSTEM FOR TRANSFORMING NON-NORMAL DATA

Y. S. Yang (Taiwan)

Received April 28, 2007

Abstract

Many statistical methods applied to the manufacturing quality control and operations management have been under the assumption that the process characteristic investigated is normally distributed. If the process characteristic is not normally distributed, a common practice is to transform the non-normal data into a normal one. In this paper, we investigate how the Johnson transformation made by the choice of the z-value in M procedure and present the some properties of selected z-value for various distributions. We also evaluate the transformation based on the successful fitting rates under Shapiro-Wilk normality test. Our study centers on simulations of left-skewed, symmetric and right-skewed distributions with different kurtoses. The limitations and conclusions addressed to practitioners are provided along with simulation study on a variety of underlying distributions.

Keywords and phrases: Johnson’s system, non-normal distribution, transformation.