An adjusted boxplot for skewed distributions

The boxplot is a very popular graphical tool for visualizing the distribution of continuous unimodal data. It shows information about the location, spread, skewness as well as the tails of the data. However, when the data are skewed, usually many points exceed the whiskers and are often erroneously...

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Bibliographic Details
Published in:Computational statistics & data analysis Vol. 52; no. 12; pp. 5186 - 5201
Main Authors: Hubert, M., Vandervieren, E.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 15.08.2008
Elsevier Science
Elsevier
Series:Computational Statistics & Data Analysis
Subjects:
Distribution theory
Exact sciences and technology
General topics
Mathematics
Multivariate analysis
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in probability and statistics
Probability and statistics
Sciences and techniques of general use
Statistics
Outlier
Discriminant analysis
Data analysis
Statistical computation
Statistical distribution
Simulation
Skewness
Distribution function
Skewness measure
Approximation theory
Multivariate analysis
Coefficient of skewness
ISSN:0167-9473, 1872-7352
Online Access:Get full text
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Description
Summary:The boxplot is a very popular graphical tool for visualizing the distribution of continuous unimodal data. It shows information about the location, spread, skewness as well as the tails of the data. However, when the data are skewed, usually many points exceed the whiskers and are often erroneously declared as outliers. An adjustment of the boxplot is presented that includes a robust measure of skewness in the determination of the whiskers. This results in a more accurate representation of the data and of possible outliers. Consequently, this adjusted boxplot can also be used as a fast and automatic outlier detection tool without making any parametric assumption about the distribution of the bulk of the data. Several examples and simulation results show the advantages of this new procedure.
ISSN:0167-9473
1872-7352
DOI:10.1016/j.csda.2007.11.008