CINTERVAL Subcommand (MANOVA: Multivariate command)

In addition to the specifications described in MANOVA: Univariate, the keyword MULTIVARIATE is available for multivariate analysis. You can specify a type in parentheses after the MULTIVARIATE keyword. The following type keywords are available on MULTIVARIATE:

ROY. Roy’s largest root. An approximation given by Pillai 1 is used. This approximation is accurate for upper percentage points (0.95 to 1), but it is not as good for lower percentage points. Thus, for Roy intervals, the user is restricted to the range 0.95 to 1.

PILLAI. Pillai’s trace. The intervals are computed by approximating the percentage points with percentage points of the F distribution.

WILKS. Wilks’ lambda. The intervals are computed by approximating the percentage points with percentage points of the F distribution.

HOTELLING. Hotelling’s trace. The intervals are computed by approximating the percentage points with percentage points of the F distribution.

BONFER. Bonferroni intervals. This approximation is based on Student’s t distribution.

  • The Wilks’, Pillai’s, and Hotelling’s approximate confidence intervals are thought to match exact intervals across a wide range of alpha levels, especially for large sample sizes 2. Use of these intervals, however, has not been widely investigated.
  • To obtain multivariate intervals separately for each parameter, choose individual multivariate intervals. For individual multivariate confidence intervals, the hypothesis degree of freedom is set to 1, in which case Hotelling’s, Pillai’s, Wilks’, and Roy’s intervals will be identical and equivalent to those computed from percentage points of Hotelling’s T 2 distribution. Individual Bonferroni intervals will differ and, for a small number of dependent variables, will generally be shorter.
  • If you specify MULTIVARIATE on CINTERVAL, you must specify a type keyword. If you specify CINTERVAL without any keyword, the default is the same as with univariate analysis—CINTERVAL displays individual-univariate confidence intervals at the 0.95 level.
1 Pillai, K. C. S. 1967. Upper percentage points of the largest root of a matrix in multivariate analysis. Biometrika, 54, 189-194.
2 Burns, P. R. 1984. Multiple comparison methods in MANOVA. In: Proceedings of the 7th SPSS Users and Coordinators Conference. : .