SPLIT-PLOT DESIGN

a ONI —

TABLE 8.14-3 Partitioning of Error Terms
for Tests of Homogeneity
NI A A ———— —

O liže (be)

SS; Ww.Sroup di — x : gr — Ungr
df <n—l žy; s 2 Ža 2
AS, ;
44 (ABS im)? 4 (AB )? LI ( m ( »)
SSy x subj w.group a; — Ma —— — Žena — z—— —t '

1 nr H gr nar

df<(n - IXa- l)

LAJA 2 Ci z
AS ji A, ;
ACS jam? zl4la" (iš m) Ne )
H 1

U ,.a (
SS, x ubi w.grovp a, T ma a ng gr ngr
df < (n — IXYr — bh)
g rn «ar (ABC a)? de (ABS, a? s (4CS m)?
SSgc x subj w.group a, — ME JABCSI em — ba ZME — xa. a H xž U
uni 4 raki ia 4
(5 H 2 a 2
AS eni A,j
m s (AB, )? y dla? n s ba: Na ) Ho s)
to nr O ng 1 ar nar

dt — (n — 1Xg — IXr — 1)
a a vv vv zv —,

TABLE 8.14-4 Conservative F Ratio Degrees of Freedom
a  ŽIDODIY————

Numerator of F ratio df

a o v v —
MS; 1, pin — b)
MS,; (p - D.pla— b)
MS« 1, fa — 1)
MS;,e p-li.mMdn-Il
MSgc . 1, pin — 1)
MS ac p-l,pa-1l)

La v nn nn ooo 6 —5——

interaction is significant, the experimenter might want to test the signifi-
cance of simple-simple main effects and simple interaction effects. These
tests are outlined in Table 8.14-5. The formulas are given for the first
level of each treatment only. The formulas at other levels of the treatments
follow the pattern given for the first level. The error terms appearing in
Table 8.14-5 for each test are appropriate for a mixed model.

The rationale underlying the selection of a denominator for F ratios
is presented in Section 8.6. The reader should be certain that he under-
stands the principles on which the determination of the correct error
terms is based. The terms given in the table are only correct for the mixed
model in which A, B, and C are fixed effects and subjects are random
effects. No dificulty should be encountered in determining the error term
for other models if one remembers that

zrotR Nia RED enja ja SR