In multivariate fits, the sums of squares due to hypothesis and error are matrices of squares and cross products instead of single numbers. And there are lots of ways to measure how large a value the matrix for the hypothesis sums of squares and cross products (called H or SSCP) is compared to that matrix for the residual (called E). JMP reports the four multivariate tests that are commonly described in the literature. If you are looking for a test at an exact significance level, you might need to go hunting for tables in reference books. Fortunately, all four tests can be transformed into an approximate F test. If the response design yields a single value, or if the hypothesis is a single degree of freedom, the multivariate tests are equivalent and yield the same exact F test. JMP labels the test Exact F. Otherwise, JMP labels it Approx. F.

In the golf balls example, there is only one effect, so the Whole Model test and the test for Brand are the same, which show the four multivariate tests with approximate F tests. There is only a single intercept with two DF (one for each response), so the F test for it is exact and is labeled Exact F.

The red triangle menus on the Whole Model, Intercept, and Brand reports contain options to generate additional information, which includes eigenvalues, canonical correlations, a list of centroid values, a centroid plot, and a Save command that lets you save canonical variates.

The effect (Brand in this example) pop-up menu also includes the option to specify contrasts.

The custom test and contrast features are the same as those for regression with a single response. See the Standard Least Squares Report and Options topic.

To see formulas for the MANOVA table tests, see Multivariate Tests.