Examining Associations between Views of a Data Set

DM[S-8,504~359 and DOE grant Connecting viewa.is one of the techniques for the exploration of multivariate data. In this paper I review painting as a technique for connecting views. I then describe the odds plot, a new graphical display to be used in conjunction with painting. It is designed to emphasize associations between views. Permutation tests offer a way of assessing whether an observed association should be taken seriously. Examples illustrate the use of painting and odds plots. 1 Introduction Detecting structure in multivariate data is one of the fundamental problems in data analysis. Structure can have a variety of meanings: Clustering, associations between variables, presence of outliers, etc. Precisely what aspects of a data set we are interested in will depend on the underlying scientific problem. In any case, looking at a printout of hundreds or thousands of numbers is not a viable way of gaining insight. The data have to be either numerically summarized or graphically presented. Any numerical summary conveys an accurate impression of the data distribution only under certain assumptions; if these assumptions are. violated, the summary can be misleading ;. Mean vector and covariance. matrix, for example,do not provide an accurate picture ofa data setconsistingoftwo spaciallyseparated, spherical clusters. If weare in an exploratory situation, graphical presentation clearly is the better approach. Unfortunately it is not easy to visually present a multivariate data set. This difficulty is reflected in the large number of displays that have been invented (see Gnanadesikan (1977) for examples). An alternative is to give up on the attempt of squeezing all the information into a single view, and instead display multiple views of the data. Multiple views can be displayed sequentially (this is a way of thinking about rotating three dimensional scatterplots) or simultaneously. In this paper I will focus on the simultaneous display of views. Suppose we have a data set four variables,. X 4 • We could display the data in two bivariate scatterplots, for example a plot of Xz against Xl (Plot-1) and a. plot of X 4 versus X 3 (Plot-2). Every observation now is represented by two icons, one in Plot-1 and oneinPlot-2. The information contained in those two plots, however, is not in itself sufficient to reconstruct the configuration ofthe data in four dimensional space-for reconstruction we need to be able to connect the two views, Le, identify pairsofjcons{one in each plot) corresponding to the same observation. …