Statistica Sinica 8(1998), 813-826

BIVARIATE QQ-PLOTS AND SPIDER WEB PLOTS

John I. Marden

University of Illinois

Abstract: QQ-plots are extremely useful in univariate data analysis. In this article, Koltchinskii (1997) and Chaudhuri's (1996) definition of multivariate quantile is used to develop analogous plots for bivariate data. Bivariate qq-plots are exhibited for comparing a sample to a given population distribution (the bivariate normal), and for comparing two or more bivariate samples. The plots are based on drawing arrows from the quantiles in one distribution to the corresponding quantiles in the other. These plots can reveal differences in location, scale and skewness, as well as outliers. Spider web plots are introduced for plotting a systematic set of quantiles for a single sample without having to specify a reference population distribution.

Key words and phrases: Arrow plots, bivariate qq-plots, bivariate quantiles, bivariate ranks, spider web plots.