A Modified Adjusted Boxplot for Skewed Distributions

• Activity Number: 682
• Type: Contributed
• Date/Time: Thursday, August 5, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Graphics
• Author(s): Yinaze Herve Dovoedo*+ and Subhabrata Chakraborti
• Companies: The University of Alabama and The University of Alabama
• Keywords: Boxplot ; Fences ; Outlier detection ; Semi-interquartile range (SIQR) ; Median ; Medcouple (MC).

Abstract

The traditional boxplot is a popular tool for the display and summary of univariate data. It is also used for the detection of possible outliers. While not explicitly assumed, the boxplot works well when the underlying distribution is symmetric so the data have similar behavior in the tails. It is well documented that when the distribution is skewed, the application of the boxplot results in increased false alarms. In this article, a modification of the adjusted boxplot for skewed distributions along the lines of Hubert and Vandervieren (2008) is presented. The fences are constructed using multiples of the upper and the lower semi-interquartile ranges (SIQR), respectively, measured from the sample median. The multiples are functions of a robust measure of skewness called the medcouple (MC). Examples are given for illustration of the proposed method. Also, a simulation study is performed.