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The Bagplot: A Bivariate Boxplot

Peter J. Rousseeuw, Ida Ruts and John W. Tukey
The American Statistician
Vol. 53, No. 4 (Nov., 1999), pp. 382-387
DOI: 10.2307/2686061
Stable URL: http://www.jstor.org/stable/2686061
Page Count: 6
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Abstract

We propose the bagplot, a bivariate generalization of the univariate boxplot. The key notion is the halfspace location depth of a point relative to a bivariate dataset, which extends the univariate concept of rank. The "depth median" is the deepest location, and it is surrounded by a "bag" containing the n/2 observations with largest depth. Magnifying the bag by a factor 3 yields the "fence" (which is not plotted). Observations between the bag and the fence are marked by a light gray loop, whereas observations outside the fence are flagged as outliers. The bagplot visualizes the location, spread, correlation, skewness, and tails of the data. It is equivariant for linear transformations, and not limited to elliptical distributions. Software for drawing the bagplot is made available for the S-Plus and MATLAB environments. The bagplot is illustrated on several datasets-for example, in a scatterplot matrix of multivariate data.

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