Use the eigen analysis to assess how the response means differ among the levels of the different model terms. The eigen analysis is of E-1 H, where E is the error SSCP matrix and H is the response variable SSCP matrix. These eigenvalues are used to calculate the MANOVA tests. Place the highest importance on the eigenvectors that correspond to high eigenvalues.

For the door lock data, the first eigenvalue for Method*Plant (0.1597) is greater than the second eigenvalue (0.00473), so place higher importance on the first eigenvector. The first eigenvector for Method*Plant is 0.16117, -0.04629. The highest absolute value within this vector is for the response usability, implying that usability means have the largest difference between the factor levels for the method-by-plants interaction.