32

SPSS UPDATE 7-9

Test of simple main effects can be reguested as well. To test factor A within the B BY C treatment
combinations the following DESIGN subcommand is used:

DESIGN<B, C, B BY C, A WITHIN B(l) BY C(l),
A WITHIN B(l) BY C(2), A WITHIN B(2) BY C(l),
A WITHIN B(2) BY C(2)/

It may also be desirable to compare two or more means at particular levels of another factor or
treatment combinations. For example, it may be interesting to compare the effectiveness of drug l
with drug 2 within each patient category. Such comparisons can be performed by extending the
methods used for ordinary simple effects. The procedure is as follows:

4. Define a contrast incorporating the comparisons of interest such as

CONTRAST( DRUG) -SPECIAL(1 l 1 1 -l 0 2 -l -l)/

2 Partition the factor into the desired components by specifying
PARTITION( DRUG) /

In subseguent designs, DRUG(1) will refer to the drug | versus drug 2 comparison. DRUG(2)
will refer to the drug 1 versus drugs 2 and 3 combined comparison.

3 Reguest regression-approach sums of sguares by using
METHOD-SSTYPE (UNIOVE) /

This is mandatory even for orthogonal designs, because DRUG(1) and DRUG(2) are not
independent.

4 Specify the designs as for ordinary simple effects, but expand the simple effects terms
according to the CONTRAST/PARTITION specification:

DESIGN<CAT, DRUG(1) WITHIN CAT(l),
DRUG(l) WITHIN CAT(2),
DRUG(2) WITHIN CATUL),
DRUG(2) WITHIN CAT(2)/

Figure 1.30b presents the output for this design.

Figure 1.30b

TESTS OF SIGNIFICANCE FOR Y USING UNIOUE SUMS OF SOUARES

SOURCE OF VARIATION SUM OF SOUARES DF MEAN SOUARE F SIG. OF F
WITHIN CELLS 106.00000 i2 8.83333

CONSTANT 882 .00000 l 882 .00000 99. 84906 0.0
CAT 18.00000 1 18.00000 2.03774 -179
DRUGI l); WITHIN CATU1) 24 .00000 1 24 00000 2.71698 .125
DRUG(2) WITHIN CAT(2) 18.00000 l 18.00000 2.03774 -179
DRUG(1) WITHIN CAT(2) 96 .00000 l 96.00000 . 10.86792 -006
DRUG(2) WITHIN CATUL) 18.00000 1 18.00000 2.03774 .179

a MM omen WE EDEM REEEE ER REEEEEEEM]

1.31 MULTIVARIATE TESTS OF SIGNIFICANCE

1.32 Standard MANOVA Output

In the univariate F test, the F value is a function of the ratio (SSH)/(SSE), where SSH is the sum of
sguares due to the hypothesis and SSE the sum of sguares due to error. Significance tests in
multivariate analysis of variance models are based on functions of the eigenvalues of the matrix
S,S;!, where S, is the matrix of the sums of sguares and cross products (SSCP) for the hypothesis
and S, is the SSCP matrix for the error. The MANOVA procedure computes four statistics used for
significance tests: Roy's largest root, Wilks' lambda, Hotelling's trace, and Pillaj's criterion. (All of
these are functions of the eigenvalues.)

The MANOVA commands for the multivariate analysis are exactly the same as in the
univariate case, except that two or more response variables are specified instead of one. Figure
1.32a, given below, illustrates the use of MANOVA to analyze the dental calculus reduction data in
Finn (1974). The response variables in this example are RCAN, RLI, and RCI.