An Asymmetrically Modified Boxplot for Exploratory Data Analysis

• Activity Number: 543
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Graphics
• Author(s): Michael Walker*+ and Subha Chakraborti
• Companies: The University of Alabama and University of Alabama
• Keywords: Boxplot ; Order Statistics ; Outlier Detection ; Box Plot ; Nonparametric Statistics ; Graphics

Abstract

The boxplot, formalized by John Tukey, is a simple and effective graphical tool in many fields and disciplines. This paper highlights the origins and progression of the boxplot that is now widely used as an industry standard as well as its inherent limitations in outlier detection when dealing with asymmetric data. This background is necessary in understanding the ultimate aim of the paper, which is to present a new modification to the boxplot, the Ratio-Skewed boxplot, for use with any univariate data set, symmetric or skewed, regardless of the sample size. By incorporating an additional term to account for underlying skewness observed within the quartiles, the proposed methodology adjusts the boxplot fences in order to improve the effectiveness of the detection of outliers. Further, this additional term is shown to be highly related to the nonparametric measure of skewness known as Bowley's Coefficient. Through simulation studies this modification of the boxplot is shown to be simple and effective, as well as very consistent in outlier detection for several known distributions.