A simple more general boxplot method for identifying outliers

Abstract

The boxplot method (Exploratory Data Analysis, Addison-Wesley, Reading, MA, 1977) is a graphically-based method of identifying outliers which is appealing not only in its simplicity but also because it does not use the extreme potential outliers in computing a measure of dispersion. The inner and outer fences are defined in terms of the hinges (or fourths), and therefore are not distorted by a few extreme values. Such distortion could lead to failing to detect some outliers, a problem known as "masking". A method for determining the probability associated with any fence or observation is proposed based on the cumulative distribution function of the order statistics. This allows the statistician to easily assess, in a probability sense, the degree to which an observation is dissimilar to the majority of the observations. In addition, an adaptation for approximately normal but somewhat asymmetric distributions is suggested.