SECTION 8.14 TYPE SPF-p.gr DESIGN 299

on each subject is to randomly assign the BC treatment combinations to
gr matched subjects within each block. This latter design reguires a total
of npgr subjects.

These three-treatment designs are similar to split-split-plot designs
used in agricultural research. The essential difference is that, in a split-
split-plot design, levels of treatment A are assigned to plots (plots correspond
to blocks of subjects in behavioral research). These plots are then subdivided
for the levels of treatment B and subdivided again for the levels of treatment
C. The levels of treatment B are randomly assigned to split-plots and
levels of C are randomly assigned to split-split-plots. This randomization
procedure can be contrasted with that used for a type SPF-p.gr design,
where the BC treatment combinations are randomly assigned within each
block. The two randomization procedures lead to different error terms for
testing treatment C and all interactions involving C.

Figure 8.14-1 shows a block diagram of a type SPF-2.22 design.
The structural model for this design is

Xiam — HE Ci t Te bt B; tet aB;; £ ava By 4 oByije

t Brmgij Vami) BI TUjkmti) 7 olijkm):

j Figure 8.14-1 Block diagram of type SPF-2.22
Rt design.

Because the analysis of this, design poses computational problems
not previously discussed, a numerical example is given in Table 8.14-1,
F where the following notation is used:

p levels of a, < 2

g levels of b; < 2

ga

r levels ofc, < 2

n levels of s,, < 4

o z

The analysis is summarized in Table 8.14-2.