N SECTION 8.14 TYPE SPF-p.gr DESIGN 303

——<———— dn v cv, v. ov o

s vih v, and v, degrees of freedom.
Six variance-covariance matrices are associated with a type SPF-2.22
design —g x gata,,g x gata,, r xrat a,,rxrata,, gr x grata,,
and gr x gr at a;. In order for each of the within-subjects F ratios to be
distributed as the F distribution, all variances for a particular population
| dispersion matrix should be egual to o? and all covariances egual to po?
| Section 8.5 described procedures for determining the tenability of the
| hypotheses that, for example, (1) the g x a population matrix at level a,
— is egual to the g x g matrix at a, and (2) the pooled dispersion matrix

pom

|

| . E(MS) A, B, and C Fixed Effects,

romi MS Foo Subjects Random

| —5<—< ooo sa v vo v—,v,v,-—v,v, -,], c-,,
|
| 3.125 [$]< 200 o? ft grož 4 ngro?
1.562 ož 4 gra!
162.000 [$] < 199.51» oč t roj, t nproj
6.125 [$] — 7.54" ož -t roj, k nrol,
812 ož t roj,
24.500 [5] < 6187" ož t gol, -- npgož
10.125 [5] < 25.57" o; gaž, - ngol,
.Z96 ož t gol,
8.000... 15] < 25.64" ol dt oj, t npoj,
3.125 (i$] < 1002" O? bo ož, ht nol,,
— 312 Ni oč toj,

OU—OIA—OJ JJ ae Ži s zgo

for the two levels of A has the symmetry described above. Identical tests
can be performed for the r x r dispersion matrices and gr x gr dispersion
matrices. If the assumptions of eguality and symmetry of the variance-
Covariance matrices are not tenable, conservative F tests as presented in
Table 8.14-4 can be computed. It will be recalled from Section 8.5 that a k
Conservative F test is computed in the usual way but that the F table is
H entered with modified degrees of freedom.
s
Č
is H
s. TESTS OF SIMPLE EFFECTS ij
le

ZEM ONIHaIgI

It is apparent from Table 8.14-2 that treatments B and C, as well
as the AB, AC, BC, and ABC interactions, are significant. Because the triple