If the null hypothesis is rejected then clearly the means
of the variables X and Y are different for at least two of the
treatment groups; moreover, the distance between one or more
of the centroids is statistically significant -- i.e., U1, U2,
and U3 do not occupy the same point in vector space. In a one-way
MANOVA experiment with three dependent variables the circles
depicted above become spheres and the coordinate axes three-dimensional.
Of course, through the use of matrix algebra the number of dimensions
are only limited by the robustness of the underlying statistics
employed to determine statistical significance.