' 6 SPSS UPDATE 7-9

1.5 Specifying a Model with the DESIGN Subcommand

If the desired model is not the default full factorial, the model must be specified using the DESIGN
subcommand. To specify a model that includes only the main effect terms, use

MANOVA y BY CAT(1.2) DRUG(1.3])/
DESIGN CAT,DRUG/

Jf there are three factors, (A, B, and C) with three levels each, the model containing only main
efiects and the A BY B and B BY C interactions is specified by

MANOVA Y BYABC (1.3)/
DESIGN- A, B, C; A BY B, B BY C/

The keyword BY in the DESIGN subcommand indicates an interaction term. Thus a three-way
interaction is written as A BY B BY C.

1.6 Specifying the ERROR Term

Unless otherwise reguested, the within-cells mean sguare is used as the denominator for all the F
values. If there is no within-cells error, the residual error is used. The residual mean sguare is the
mean sguare for all terms not specified in the DESIGN subcommand. For example, if the model
containing only main effects for DRUG and CAT is reguested using

DESIGN: CAT,DRUG/

the residual error term is the mean sguare for the CAT BY DRUG interaction. For the three-factor
design specification developed previously, the residual error corresponds to the sum of sguares for
the pooled A BY C and A BY B BY C interactions since they are not included in the DESIGN
specification.

The ERROR subcommand designates the error term to be used for the analysis. See Section
1.91 for rules governing the use of the ERROR subcommand. If different error terms are to be
used for the various terms in the design specification, this is indicated in the DESIGN
subcommand. See Section 1.92 for further details.

4.7. An Example Using DESIGN and ERROR

The following commands reguest a main effects model for the data of Figure 1.2. The pooled
interaction term (denoted as R for residual) and within-cells error (denoted as W) are used as the
error.

MANOVA Y BY CAT(1,2) DRUG(1,3)/
ERROR-WtR/
DESIGN<CAT, DRUG /

The error subcommand must precede the design specification to which it applies. The analysis of
| variance table from the preceding commands is given in Figure 1.7.

Figure 1.7

TESTS OF SIGNIFICANCE FOR Y USING SEOUENTIAL SUMS OF SOUARES

SOURCE OF VARIATION SUM OF SOUARES DF MEAN SOUARE F SIG. OF F
WITHINYRESIDUAL 250 .00000 i4 17.85T14

CONSTANT 882 .00000 l 882 .00000 49.39200 0.0
CAT 18.00000 1 18.00000 1.00800 .332
DRUG 48.00000 2 24.00000 1.34400 .292

OO ODD

The result in Figure 1.7 can also be obtained by specifying

MANOVA Y BY CAT(1,2) DRUG(1,3)/
DESIGN < CAT VS WR, DRUG VS WHER/

1.8 Partitioning the Sum of Sguares

Often it is desirable to partition the sum of sguares associated with the various effects into a
number of components that are more relevant to the individual guestions of interest. See Cochran
and Cox (1957).

In procedure MANOVA partitions are controlled by the keyword PARTITION followed by
the name of the factor and the degrees of freedom associated with each component.

To partition the sum of sguares for factor DRUG into two components with one degree of
freedom each, the following commands can be used.