MANOVA 37

1.33 Optional MANOVA Output
Other output related to multivariate significance tests can be obtained by using the PRINT
subcommand. Such optional output includes
1 The error matrix. For every error matrix used in the model,
PRINT<ERROR( SSCP) / |
can be used to obtain the error SSCP matrix, S,. Although only one error matrix, the within-
cells error matrix, was used in Figure 1.32a, more than one error matrix is sometimes used

(e.g., in muitivariate nested designs). The error matrix for Figure 1.32a is given in Figure
1.33a.

Figure 1.33a

WITHIN CELLS SUM-0F-SOVARES AND CROSS-PRODUCTS

RCAN RLI RCI
RCAN 137.89515
RLI 101.90797 261.87433
RCI 81.03938 217.53449 423. 98046

The error variance-covariance and error correlation matrices can also be obtained, by
specifying
PRINT-ERROR (COV , COR) /

2 The hypothesis SSCP matrix. The matrix S, for each effect can be obtained by specifying
PRINT<SIGNIF(HYPOTH) /

This matrix is adjusted for the covariates (if any). The hypothesis SSCP matrix for the TR
effect in Figure 1.32a is given in Figure 1.33b.

Figure 1.33b

EFFECT .. TR
ADJUSTED HYPOTHESIS SUM-OF-SOUARES AND CROSS-PRODUCTS

RCAN RLI RCI
RCAN 6. 18306
RLI 8.26479 28.07315
RCI 15.81805 41.86935 69.55358

.3 Roy-Bargmann step-down analysis (Roy and Bargmann, 1958). For each effect, step-down
tests (which depend on the ordering of the response variables) can be performed by specifying

PRINT<SIGNIF ( STEPDOWN) /

The number of tests for effects in a step-down analysis is egual to the number of response
variables in the model. For the first response variable, the test statistic is the same as the
univariate F statistic. The test statistic for the second response variable is identical to the
univariate test statistic that would result if the first response variable were treated as a
covariate. The test statistic for the third response variable is adjusted for the first two
variables, and so on. A significant test statistic for the kth response variable indicates that this
variable is important for testing the hypothesis that the effect is zero and cannot be accounted
for by a linear combination of the preceding k — 1 variables. Since testing begins with the last
variable and proceeds backwards until a significant result is obtained, the variables assumed to
be important in testing an effect should appear early in the step-down ordering. MANOVA
uses the ordering of the response variables given in the MANOVA variable list. The step-down
analysis for the TR effect in Figure 1.32a is given in Figure 1.33c.

Figure 1.33c

ROY-BARGMAN STEPDOWN F - TESTS

VARIABLE HYPOTH. MS ERROR MS STEP-DOWN F HYPOTH. DF ERROR DF SIG. OF F
RCAN 1.54577 1.37895 1.12097 4 100 351
RLI 4. 78488 1.88446 2.53912 4 99 045
RCI 4.57059 2.4B108 1.84218 4 98 -127