The Normal Probability Plot as a Tool for Understanding Data: A Shape Analysis from the Perspective of Skewness, Kurtosis, and Variability


Gregory L. Boylan, Advanced Quality Engineering Laboratory, Department of Industrial Engineering, Clemson University, Clemson, SC 29634, USA.



Continuous quality improvement is an effort to improve the quality of products, processes, or services. A program intended to effectively implement such efforts begins with the collection and analysis of data. The primary purpose of the normal probability plot, which is one of the most frequently used graphical tools by quality practitioners and researchers, is for normality testing; however, the plot offers other valuable insights into data analysis that have rarely been addressed in the research community. This article provides an overview of distributional characteristics in the context of the four sample moments and investigates how variations in these moments affect the normal probability plot, focusing primarily on the presence of skewness and kurtosis and the effects of variability. This article then lays out a comprehensive analysis of how various statistical characteristics within a data set can influence the shape and corresponding properties of a normal probability plot, demonstrating how variations in the characteristics of the data can reveal or mask the degree of concavity, convexity, or the S shape in the plot, as well as the spread of the data about the mean and in the tails. This can provide engineers with a better understanding of the ways in which data “communicate” through the plot, thereby providing a better basis for initial assumptions, as well as facilitating more accurate model estimation and optimization results thereafter. Copyright © 2011 John Wiley & Sons, Ltd.