ABSTRACT
From now on there is a shift of viewpoint in that the p measurements (y i1, …, y ip ) on an individual will be treated as a single vector multivariate observation y i rather than as a set of separate univariate observations. This sounds like just shifting the furniture around, but it opens up the route to the more advanced treatment of the subject. The primary interest is still in inference about the means μij of (3.1.1) as in Anova, but these parameters are now treated as components of the p × 1 vector μ i = E(y i ). The mean-squares of Anova, which represent components of univariate variation, are now replaced by covariance matrices which represent components of multivariate covariation. The general model on which the analysis is based is y i = µ i + e i for individual i, corresponding to (3.1.1), where the errors e i , are independent with means 0 and covariance matrices V(e i ) = Σ; thus Σ is p × p with (j, k)th element C(eij, eik ) = Σ jk . Note the implication here that V(y i ) = V(e i ) = Σ is the same for all i.
