N SECTION 8.14 TYPE SPF-p.gr DESIGN 303 ââ<ââââ 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 âg 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, â 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 | â5<â< ooo sa v vo vâ,v,v,-âv,v, -,], c-,, | | 3.125 [$]< 200 o? ft groĹž 4 ngro? 1.562 oĹž 4 gra! 162.000 [$] < 199.51Âť oÄ t roj, t nproj 6.125 [$] â 7.54" oĹž -t roj, k nrol, 812 oĹž t roj, 24.500 [5] < 6187" oĹž t gol, -- npgoĹž 10.125 [5] < 25.57" o; gaĹž, - ngol, .Z96 oĹž t gol, 8.000... 15] < 25.64" ol dt oj, t npoj, 3.125 (i$] < 1002" O? bo oĹž, ht nol,, â 312 Ni oÄ toj, OUâOIAâOJ JJ ae Ĺ˝i 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 Ä 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