ABSTRACT
A multivariate observation consists of simultaneous measurement of several attributes. For example, a part coming out of a numerically controlled metal cutting lathe can be measured on several critical dimen sions. Multivariate observations are conveniently represented by vectors with p entries corresponding, to the p variables measured on each ob servation unit. This chapter discusses inferential methods applicable to multivariate normal data. In most of the chapter we assume multivariate normality of the data and present methods which enable us to produce estimates of population parameters and construct tests of hypotheses about multivariate population parameters using a simple random sam ple of multivariate observations. The analysis of multivariate data poses a challenge beyond the naive analysis of each dimension separately. One aspect of this challenge stems from the simultaneous consideration of several probability statements, such as p-tests of hypothesis. This creates a problem of multiple comparisons that requires adjustments of univariate significance levels so as to attain a meaningful overall sig nificance level. A second component of the multivariate data analysis challenge is to account for the internal correlation structure among the p-dimensions. This again affects overall significance levels.
