f

SPSS UPDATE 7-9

A The average F test. If
PRINT<SIGNIF (AVERF) /

is specified, MANOVA outputs an averaged F test for each tested effect. This is particularly
useful for repeated measures designs (see Section 1.44). The sum of sguares for the effect and
the sum of sguares for the error in the averaged F test are obtained by summing over the
hypothesis sum of sguares and the error sum of sguares, respectively, for each variable. The
averaged F test for the TR effect in the dental calculus example is given in Figure 1.33d.

Figure 1.33d

o A a a EEA ER EVER EEEEEEEEEEEEEEEEEEEEEMMEEEDEEEHH
AVERAGED F-TEST WITH (12,300) D. F.
HYPOTH, SS ERROR SS HYPOTH. MS ERROR MS F SIG. OF F
(AVER. ) 103.80979 823. 74994 8.65082 2 ;T4583 3.15052 -000

A gi MREČ RE NR EEEEEENEAEEENEEEME MENE WEEEEEEEERE WERE EOEEEEEEEEREM!

5 A brief table of multivariate significance tests. A summary table, similar to the univariate
ANOVA table, (with Wilks' lambda and the corresponding approximate F statistic replacing
the univariate F) can be obtained by specifying

PRINT-SIGNIF(BRIEF) /
Note that the BRIEF specification overrides reguests for the standard multivariate signifi-

cance tests, the hypothesis SSCP matrix, and step-down analysis. The BRIEF output for
Figure 1.32a is given in Figure l.33e.

Figure 1.33e

V ERM EME EDEM OREHI

TESTS OF SIGNIFICANCE FOR WITHIN CELLS USING SEOVENTIAL SUMS OF SOUARES

SOURCE OF VARIATION WILKS LAMBDA APPROX MULT F SIG. OF F AVERAGED F SIG. OF F
CONSTANT .46B43 37.07044 0.0 76.86413 0.0
YEAR 95923 1.38845 .251 2 .83448 038
TR .B0733 1.82255 045 3.15052 000
YEAR BY TR 97555 81881 .487 1.32601 266

V A NA AEIE NEKE MANE WED ES NEEEEEEWEEEENONE

1.34 Principal Components Analysis

Principal components analysis (which is performed on each'error matrix used in the model) can be
reguested via the PRINT subcommand. If

PRINT-PRINCOMPS ( COR) /

is specified, the principal components of the error correlation matrix are printed, while
PRINTPRINCOMPS( COV ) /

produces the principal components of the error-covariance matrix.
The output for a principal components analysis includes

1 A table listing the eigenvalues of the error matrix (COR or COV) and the proportion and
cumulative proportion of the total variance accounted for by each component.

2 The principal components of the error matrix.

3 The determinant of the error matrix, the Bartlett test of sphericity, and F max tests. The
Bartlett test statistic, which has an approximate chi-sguare distribution with g(g — 1)/2
degrees of freedom, is used to test the hypothesis that the population error correlation matrix
is an identity matrix (or, eguivalently, that the population error variance-covariance matrix is
a diagonal matrix). The F max statistic (the ratio of the largest to the smallest diagonal
element of the error variance-covariance matrix) is used to test the hypothesis that the
variances of the g response variables are egual. The critical points of the distribution of F max
under the null hypothesis can be found in Winer (1971) and depend on g and n,. Both the
Bartlett test and F max test can be obtained simply by reguesting the error correlation matrix;
i.e., by specifying

PRINT-ERROR/(COR) /

in a MANOVA run. It is not necessary to perform a principal components analysis in order to
obtain these statistics.