On Some Properties of a Simple and More General Boxplot-Type Method for Identifying Outliers

• Activity Number: 471
• Type: Contributed
• Date/Time: Wednesday, August 5, 2009 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Graphics
• Author(s): Yinaze H. Dovoedo*+ and Subhabrata Chakraborti
• Companies: The University of Alabama and The University of Alabama
• Keywords: boxplot ; outlier ; identification ; fence ; SIQR ; median

Abstract

This paper focuses on the detection of outliers using a boxplot. The proposed method takes into account the underlying distribution and controls the probability that one or more observations in a random sample are wrongly classified as outliers (see e.g., Sim, Gan and Chang (2005)). However, instead of constructing the fences using the upper and lower quartiles and a multiple of the usual IQR, for near normal and somewhat asymmetric distributions, a multiple of the upper and the lower semi-interquartile ranges (SIQR), respectively, measured from the sample median (see e.g., Schwertman et al. (2004), Kimber (1990)) are used. An exact expression for the required probability is derived for the family of location-scale distributions. This can be used to find the necessary constant for the outlier detection rule; tables are provided along with some comparisons.