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Illustration of One-way Factor Design

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.

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