PN SECTION 8.12 INTRODUCTION TO TYPE SPF-pr.g DESIGN 283

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- B, and AB comparisons should be considered. In a split-plot design, the
d, B and AB effects are usually estimated more accurately than the A effects.
This results from the fact that variation within a block is usually smaller
than variation among blocks. The average standard error of a difference is
egual for both the randomized block factorial design and the split-plot
design. Thus the increased accuracy of the B and AB effects estimates is
obtained by sacrificing accuracy on the A effects. If the experimenter is
as interested in the A effects as he is in the B and AB effects, the randomized
block factorial design should be used. It should also be noted that the
F ratio denominator degrees of freedom for A, B, and AB in the randomized
block factorial design are larger than the corresponding degrees of freedom
in a split-plot design.

A numerical index of relative efficiency of the two designs, disregard-
ing differences in degrees of freedom, is given by the following formulas
Tr: (Federer, 1955, 274). The data used in this example are from Table 8.2-2.

A efficiency

— [Pp TT VMS,.; w.groups -b pin TU DMS,  subj w.groupsl/(P4 ul )

S ubi w.groups
IH [(2 — 1)1.562 -- 2(4 — 1).507]/[(2X4) — 1] IH .658

Ji 1.563 1.563

— 42.1 percent.
B and AB efficiency

— [Pp TT I)MS,,; w.groups bt pin nn IMS,,. subj w.groupsl/(P4 TU l)

MS, x subj Ww.groups
— ((2- 11.563 -- X4 — 1).507]/[(2X4) — 1] — .658
H " 507 —. 507

x 100

x 100

z 129.8 percent.

Hence, in this example, a test of the A treatment is less than half as efficient
in the split-plot design as it is in the randomized block factorial design.
On the other hand, the B and AB tests are more efficient in the split-plot
design. The relative efficiency of tests is a basic consideration in the design
of experiments.

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d 8.12 HINTRODUCTION TO
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is The split-plot design described so far in this chapter has had two
ent treatments. The general analysis procedure for a two-treatment split-plot

A, design can be extended to designs having three or more treatments.

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