Variables Y1 to Y9 are the nine response variables. The WSFACTORS subcommand indicates that
there are two within-subjects factors, each having three levels. The order in which the variables are
specified in the WSFACTORS list is very important since it indicates the levels of PERIOD and
DIAL corresponding to Yl to Y9. The following table gives the correspondence between the
variables:

Variable PERIOD  DIAL
Y, 1 1
Y. 1 2
Y, 1 3
Y, 2 1
Y; 2 2
Y, 2 3
Y, 3 1
Y, 3 2
Y, 3 3

If the order of the two within-subjects factors is reversed in the WSFACTORS subcommand, the
PERIOD and DIAL headings must be interchanged in the above table. For example, Y; would
correspond to DIAL level 3 and PERIOD 1.

The WSDESIGN subcommand specifies the model for the within-subjects factors. The model
fit need not be saturated. To specify an additive model, use

WSDESIGN < PERIOD DIAL/

The subcommand ANALYSIS(REPEATED) indicates that a repeated measures analysis is
desired. The model for the between-subjects factors is specified, as always, by the DESIGN
subcommand. Since there is only one between-subjects factor in this experiment, the command is
DESIGN - NOISE.

The subcommand PRINT < SIGNIF(BRIEF) reguests printing of brief muitivariate output.
Excerpts from this output are shown in Figure 1.49.

Figure 1.49

EN ENE EO O

TESTS OF SIGNIFICANCE FOR Yl USING SEOUENTIAL SUMS OF SOUARES

SOURCE OF VARIATION SUM OF SOUARES DF MEAN SOUARE : F SIG. OF F
WITHIN CELLS 2491.11111 4 622.777118

CONSTANT 105868. 16667 1  105868.16667 169.99349

NOISE 468. 16667 1 468.16667 -715174

TESTS OF SIGNIFICANCE FOR WITHIN CELLS USING SEOUENTIAL SUMS OF SOUARES

SOURCE OF VARIATION WILKS LAMBDA APPROX MULT F SIG. OF F AVERAGED F SIG. OF F
PERIOD -05060 28. 14526 »011 65. 38884

NOISE AND PERIOD .15607 8.11102 062 5.67077

TESTS OF SIGNIFICANCE FOR WITHIN CELLS USING SEOUENTIAL. SUMS OF SOVARES

SOURCE OF VARIATION WILKS LAMBDA APPROX MULT F SIG. OF F AVERAGED F SIG. OF F
DIAL -01614 91.45623 -002 89.82316

NOISE AND DIAL 56498 1.15495 .425 1.90737

TESTS OF SIGNIFICANCE FOR WITHIN CELLS USING SEOUENTIAL SUMS OF SOUARES

SOURCE OF VARIATION WILKS LAMBDA APPROX MULT F SIG. OF F AVERAGED F SIG. OF F
PERIOD BY DIAL . 00075 331.44500 041 . 33566

NOISE AND PERIOD BY DIAL 00043 581.87500 031 35664

Wilks' lambda (with the corresponding approximate F) can be used to test for within- subjects
factor effects, if the compound symmetry assumption appears to be violated. The averaged F
statistics in the output are identical to the univariate mixed-model results displayed in Figure 1.47b.

Testing the hypothesis of compound symmetry is eguivalent to testing the hypothesis that the
covariance matrix of the transformed variables is a diagonal matrix (Bock, 1975, p. 459). Thus, the
Bartlett test for sphericity can be used. MANOVA performs this Bartlett test for the transformed
variables if the TRANSFORM or WSDESIGN subcommand is present.

MANOVA also perforii> the analysis of covariance on repeated measures data. If the
covariates are constant over the repeated measures, only between-subjiect factors are adjusted; and
if the covariates vary across the repeated measures, both between- and within-subjects factors are
adjusted.

MANOVA 51