The calculation of a multivariate analysis of variance (MANOVA) is essentially similar to the calculation of a univariate analysis of variance (ANOVA). In an ANOVA, the total sum of squared deviations about the grand mean – written SS (Total) – is partitioned into a sum of squares due to one or more sources and a residual sum of squares. Associated with each partition is a number, called the degrees of freedom (d.f.), representing the number of linearly independent contrasts or alternatively the number of linearly independent parameters for that source. Multivariate test procedures are based on comparisons of the matrices R and R0. This chapter introduces a technique known as canonical variates analysis (CVA). This is essentially a technique for choosing those linear compounds of the multivariate response which demonstrate the greatest inconsistency between null hypothesis and data. CVA produces a best two-dimensional approximation in the least-squares sense.