2.1. Introduction

Graphical techniques have become an integral part of any data analysis, especially now due to a tremendous increase in the accessibility to computing facilities. In general it is easy to use graphical methods for data with one, two, or even three variables. However, for multivariate data in dimensions higher than three, data reduction to two or three variables is needed before it is possible to plot them. Several methods to represent multivariate data are available in the literature. This chapter covers four of these methods in Sections 2.2 through 2.5. It may be mentioned that Section 2.5 may require a slightly higher level of familiarity with matrix decompositions and may be skipped at first reading. See Friendly (1991) for details on various other graphical methods.

The multivariate normal distribution is a basis for most of the theory on testing of hypotheses in multivariate analysis. Often graphical methods are used to assess the multivariate normality and to detect multivariate outliers. These methods are covered in Sections 2.6 and 2.7 respectively.

The probability density function of a bivariate normal distribution and the contours of the probability density function drawn graphically give information about the magnitude of the variances and correlation between the two variables. Section 2.8 discusses these graphs briefly. SAS/INSIGHT software, an interactive tool for graphical data analysis, is briefly discussed at the end of the chapter.

For illustration purposes, we have confined ourselves to the data set from Rao (1948). This data set, given in Table 1.1, consists of weights of cork boring taken from the north (N), east (E), south (S), and west (W) directions of the trunks of 28 trees in a block of plantations.