This animated series of plots illustrate the essential ideas behind the computation of hypothesis tests in a one-way MANOVA design and how these are represented by Hypothesis - Error (HE) plots.

For the multivariate linear model, **Y = X B + U**, hypothesis tests
are based on the sums of squares and crossproducts matrices for hypothesis (**H**)
and error (**E**):

There are three main steps in the animation, shown by data ellipses:

- Calculating the
**E**matrix can be viewed as first shifting the data for each group to the centroid (grand mean) of the data. - Next, the separate within-group covariance matrices
are averaged ("pooled") to give the
**E**matrix. - Finally, the
**H**matrix is visualized by starting with all groups centered at the grand mean, and moving finally to their positions in the data.