There are cases in multivariate response models, such as a repeated measures model, that allow transformation of a multivariate problem into a univariate problem (Huynh and Feldt 1970). Using univariate tests in a multivariate context is valid in the following situations:
• If the response design matrix M is orthonormal (M´M = Identity).
• If M yields more than one response the coefficients of each transformation sum to zero.
• If the sphericity condition is met. The sphericity condition means that the M-transformed responses are uncorrelated and have the same variance. M´ΣM is proportional to an identity matrix, where Σ is the covariance of the Y variables.
If these conditions hold, the diagonal elements of the E and H test matrices sum to make a univariate sums of squares for the denominator and numerator of an F test. Note that if the above conditions do not hold, then an error message appears. In the case of Golf Balls.jmp, an identity matrix is specified as the M-matrix. Identity matrices cannot be transformed to a full rank matrix after centralization of column vectors and orthonormalization. So the univariate request is ignored.
For an example of univariate and sphericity tests, see Example of Univariate and Sphericity Test.