In multivariate response model 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 option 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 “Standard Least Squares Models”.
To see formulas for the MANOVA table tests, see Statistical Details for Multivariate Tests.
The extended Multivariate Report contains the following columns:
Test
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.
Value
Value of each multivariate statistical test in the report.
Approx. F (or Exact F)
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.
NumDF
Numerator degrees of freedom.
DenDF
Denominator degrees of freedom.
Prob>F
Significance probability corresponding to the F-value.
Note: For more information about the Sphericity Test table, see Univariate Tests and the Test for Sphericity.