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Where [[Partition of sums of squares|sums of squares]] appear in univariate analysis of variance, in multivariate analysis of variance certain [[positive-definite matrix|positive-definite matrices]] appear. The diagonal entries are the same kinds of sums of squares that appear in univariate ANOVA. The off-diagonal entries are corresponding sums of products. Under normality assumptions about [[errors and residuals in statistics|error]] distributions, the counterpart of the sum of squares due to error has a [[Wishart distribution]].
== Hypothesis Testing ==
First, define the following <math display="inline">n\times q</math> matrices:
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