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 may 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 effect (Brand in this example) popup menu also includes the option to specify contrasts.
Labels each statistical test in the table. If the number of response function values (columns specified in the M matrix) is 1 or if an effect has only one degree of freedom per response function, the exact F test is presented. Otherwise, the standard four multivariate test statistics are given with approximate F tests: Wilks’ Lambda (Λ), Pillai’s Trace, the Hotelling-Lawley Trace, and Roy’s Maximum Root.
F-values corresponding to the multivariate tests. If the response design yields a single value or if the test is one degree of freedom, this is an exact F test.

Help created on 9/19/2017