di ocni;

Figure 1.47a
RUN NAME UNIVARIATE ANALYSIS OF REPEATED MEASURES DESIGN.
COMMENT DATA ARE TAKEN FROM WINER(1971) PAGE 546.

VARIABLE LIST NOISE SUBJECT PERIOD DIAL Y
INPUT FORMAT  FIXED(4Fl.0,1X,F2.0)

N OF CASES 54
INPUT MEDIUM CARD
MANOVA Y BY NOISE(l1,2) SUBJECT(1,3) PERIOD DIAL(1,3)/

DESIGN-NOISE VS l, SUBJECT W NOISE<l, PERIOD VS 2,
DIAL 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 NOISE-4,
š NOISE BY PERIOD BY DIAL VS 4/

READ INPUT DATA

llll 45

1ll2 53

l1li3 60

1121 40

1122 52

2322 39
2323 57
2331 31
2332 29
2333 46
FINISH

Figure 1.47b

TESTS OF SIGNIFICANCE FOR Y USING SEGUENTIAL SUMS OF SOUARES

.435

-000
.029

0.0
210

-850

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

CONSTANT 105868. 16667 l  105868.16667

ERROR l 2491.1111l 4 622.77T78

NOISE 468. 16667 l 468. 16667 .T5174
ERROR 2 234. 88889 8 29.36111

PERIOD 3T22.33333 2 1861.16667 63. 38884
NOISE BY PERIOD . 333.00000 2 166.50000 5.67077
ERROR 3 105.55556 8 13.19444

DIAL 2370.33333 2 1185.16667 89.82316
NOISE BY DIAL 50.33333 2 25.16667 1.90737
ERROR 4 127.11111 16 7. 94444

PERIOD BY DIAL 10.66667 4 2.66667 33566
NOISE BY PERIOD BY DIAL 11.33333 4 2.83333 35664

.B36

The mixed-model analysis reguires that the variances of the dependent variable be egual for
all factor combinations, and that the correlations of the dependent variable at different
combinations of within-subjects factors be egual. The MANOVA procedure provides a test,
discussed in the next section, for this assumption of compound symmetry.

If compound symmetry appears to be violated, the multivariate approach can be used. In
general, the univariate approach is somewhat more powerful, especially for small sample sizes.
Note that in the MANOVA procedure, the univariate results can be obtained from the multivariate
analysis output. This is important since the multivariate specifications are much simpler than the
univariate mixed- model approach just outlined.

1.48 Trend Analysis

Since both PERIOD and DIAL are statistically significant, one may wish to investigate the growth
trends for PERIOD and DIAL. If a trend analysis for PERIOD is desired, this effect can be
partitioned into a linear effect, PERIOD(1), and a guadratic effect, PERIOD(2), by using the
following specifications.

CONTRAST (. PERIOD ) <POLYNOMIAL/
PARTITION( PERIOD) /

Egually spaced PERIOD levels are assumed here; for the use of CONTRAST and PARTITION
subcommands when levels are unegually spaced, see Sections 1.88 and 1.89.

As shown in Table 1.47, the test for a PERIOD effect used the PERIOD x (subject within
NOISE) error term. For the orthogonal polynomial components of PERIOD, we can either use
this error term to test for PERIOD(1) and PERIOD(2) effects or decompose PERIOD X (subject

MANOVA

49