Pijte:

50 SPSS UPDATE /-9

within NOISE) into PERIOD(1) x (subject within NOISE) and PERIOD(2) x (subject within
NOISE) and use these as the error terms for PERIOD(1) and PERIOD(2), respectively. The
choice of procedure depends in part on the assumptions of the model (see Bock, 1975, p. 460).
Unless PERIOD(1) x (subject within NOISE) and PERIOD(2) x (subject within NOISE) both
have a fairly large number of degrees of freedom, the single error term PERIOD X (subject within
NOISE) is generally used because this test is more powerful.

ALI interaction terms containing PERIOD can also be partitioned; for example, NOISE x
PERIOD has two components, NOISE x PERIOD(1) and NOISE x PERIOD(2), and the pooled
and separated error terms described above may be used to test for these two effects. The
MANOVA specifications for trend analyses of PERIOD and DIAL are presented in Figure 1.48a,
and the resulting ANOVA table is displayed in Figure 1.48b.

Figure 1.484

O POET EPO OJ EPO JE PP O SE AERO V OENEPANNK |

MANOVA Y BY NOISE(l,2) SUBJECT(1,3) PERIOD DIAL(1,3)/
CONTRAST( PERIOD) <POLYNOMIAL /
CONTRAST (DIAL,) <POLYNOMIAL /

PARTITION(PERIOD) /

PARTITION(DIAL) /

DESIGNeNOISE VS l, SUBJECT W NOISE<l, PERIOD(l) VS 2,
PERIOD(2) VS 2, DIAL(l) VS 3,
DIAL(2) VS 3, PERIOD BY SUBJECT W NOISE«2,
DIAL BY SUBJECT W NOISE<3, NOISE BY PERIOD VS 2,
NOISE BY DIAL VS 3, PERIOD BY DIAL VS 4,
PERIOD BY DIAL BY SUBJECT W NOTSE-4,
NOISE BY PERIOD BY DIAL VS 4/

Eo ET MNE EO o RE JE PT O ES NV |

Figure 1.48b

O JO A O O PE PE EP SN Ni PR

TESTS OF SIGNIFICANCE FOR Y USING SEOUENTIAL SUMS OF SOUARES

SOURCE OF VARIATION SUM OF SOUARES DF MEAN SOVARE F SIG. OF F
RESIDUAL 0.0 o .

CONSTANT 105868. 16667 1 105868.16667

ERROR l 2491.11lll 4 622 .7T118

NOISE 468. 16667 I 468. 16667 | 75174 .435
ERROR 2 234. 88889 8 29.36111

PERIOD(l) 3721 .00000 l 3721.00000 126.73226 0.0
PERIOD(2) 1.33333 1 1.33333 04541 .B37
NOISE BY PERIOD 333.00000 2 166.50000 5.67077 .029
ERROR 3 105.55556 8 13.19444

DIAL(l) 2256 .25000 1 2256 .25000 171.00000 0.0
DIAL(2) 114.08333 l 114.08333 8.64632 019
NOISE BY DIAL 50.33333 2 25. 16667 1.90737 -210
ERROR 4 127.1111l 16 T.94444

PERIOD BY DIAL 10.66667 4 2.66667 : . 33566 850
NOISE BY PERIOD BY DIAL 11.33333 4

2.83333 .35664 836

a pp NA A AN AE NE EMA AEEENNEEE EME CENENE RO EEEEEEEERAMEEEEEAMEENH

1.49 The Multivariate Approach

In the multivariate analysis of repeated measures designs, the responses of a case are treated as an
h-dimensional response vector. In the current example each subject responds to nine variables,
each variable representing a unigue DIAL and PERIOD combination. Thus the design for Table
1.46 can be treated as a multivariate one-way design with NOISE as the grouping variable. The
model can be written as

Y; z nt a; t Ej

where Y;; < (Yi ... Yin)", o; is the treatment effect and the c;; are the errors (assumed to be
independent with an h-variate normal distribution having mean 0 and a covariance matrix Ž). As
long as ž is positive definite, the covariance structure of the Y;, can have any pattern. This
assumption is of course much less restrictive than the mixed-model assumption of compound
symmetry.

The following SPSS MANOVA commands can be used to perform a multivariate analysis of
the repeated measures data in Table 1.46.

MANOVA Yl TO Y9 BY NOISE(1,2)/
WSFACTORS s PERIOD(3), DIAL(3)/
WSDESIGN < PERIOD DIAL PERIOD BY DIAL/
PRINT < SIGNIF(BRIEF)/
ANALYSIS( REPEATED) /
DESIGN < NOISE