Advances and Applications in Statistics
Volume 8, Issue 1, Pages 57 - 71
(February 2008)
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EVALUATION OF JOHNSON?S SYSTEM FOR TRANSFORMING NON-NORMAL DATA
Y. S. Yang (Taiwan)
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Abstract: Many statistical methods applied to the manufacturing quality control and operations management have been under the assumption that the processcharacteristicinvestigatedisnormallydistributed.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 thez-value in M procedure and present the some properties of selectedz-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 addressedto practitioners are provided along with simulation study on a variety of underlying distributions. |
Keywords and phrases: Johnson?s system, non-normal distribution, transformation. |
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