306 SPLIT-PLOT DESIGN

LN DON —————

4

$SS, for b; < SS, -- SS,s

1
a r
$)SS, for bc < SS, NE SS, na SS,c d SS sc
11

$SS,s for C, — SS,g - SS ac:
1

One can see that whenever the main effects have difierent error terms,
these error terms are pooled in testing the simple main effects. The error
terms in Table 8.14-5 are given as weighted pooled mean sguares divided
by their pooled degrees of freedom. For example, the error term for testing
SS, at b, can be computed by either of the following formulas:

MS,.sj w.groups t MS, x subj v grvpsi Ii b) — 1.562 bt 812(1), —l 187
4 2
SS,tj w.groups ft SS x subj w.groups 9.375 ft 4.875 —<l 188

dn -l) spna- ia—- D — 23) 4 8X) O

The two answers agree within rounding error.

COMPARISONS AMONG MEANS

Tests of differences among means follow the procedures described
in Section 8.7. For example, the error term for Tukey's ratio for the com-
parison V < A, — A, is

MS,.si w.groups
» ngr :

The divisor, nar, is the sample size for A,. The comparison | — AB,, —
AB,, has as its error term

MS,.sj w.groups EH MS, x subj sara] To b
nr(a)

The term [MS,,sj wgroups "5 MSpxsubj w.groups(4 — )]/4 is the F ratio
denominator for testing MS, at b;. The term nr < 8 is the number of
scores in each cell of the AB Summary Table.

EXPECTED VALUES OF MEAN SOUARES

The expected values of mean sguares for Models I, II, and III can
be determined from Table 8.14-6. The terms l — p/P, 1 — g/O, | — r/R,