The Analysis of Association Among Many Variates

Summary The methods used to estimate the nature and form of linear relations among sets of variates are developed in a simple manner based on a multivariate extension of the analysis of covariance. The link between these methods of analysis and the canonical analysis is discussed; it is shown how the two analyses can complement each other. Since it is of practical importance to represent the association among the variates in terms of a minimal set of derived variates, various tests of significance for the adequacy of such sets are presented. The methods make no use of non-central distributions, the only distribution theory involved being that of determinantal ratios whose three parameters are effectively the numbers of variates in the two associated sets and the number of observations of each. The methods have been set out in enough detail to show that they are not only relevant to many practical situations but also readily computable.