Grouped Multivariate Data: Multivariate Analysis of Variance and Discriminant Function Analysis
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Investigators in many disciplines frequently collect multivariate data on samples from different populations. In Chapter 5, for example, a set of data was introduced in which an archaeologist had made four measurements on Egyptian skulls from five different epochs. A variety of questions might be asked about such data and, correspondingly, there are a variety of (overlapping) approaches to their analysis. In many examples the prime interest will be in assessing whether the populations involved have different mean vectors on the measurements taken. For this, multivariate analogues of the familiar univariate t-test, Hotelling’s T2, or analysis of variance, multivariate analysis of variance, are available. A further question that is often of interest for grouped multivariate data is whether or not it is possible to use the measurements made to construct a classification rule derived from the original observations (the training set) that will allow new individuals having the same set of measurements, but no group label, to be allocated to a group in such a way that misclassifications are minimized. The relevant technique is now some form of discriminant function analysis.
KeywordsDiscriminant Function Sudden Infant Death Syndrome Canonical Variate Multivariate Normal Distribution Discriminant Function Analysis
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