246

SPLIT-PLOT DESIGN

A nm

A COMPARISON OF THREE
FACTORIAL EXPERIMENTS

A graphic comparison of three experimental designs—a completely
randomized factorial design, a randomized block factorial design, and a
split-plot design—is shown in Figure 8.1-l. In this figure the split-plot

4, 4, a, dd 4; MX
b, b, ob; b, ob, o bp b, o b, ob; b, ob, ob;
absjsjsj o psbsjahslej absjsjs
a, od 4, Hd
(a) Type CRF-23 design (b) Type RBF-23 design (c) Type SPF-2.3 design

Figure 8.1-1 Comparison of three types of

designs.

repeated measures design is designated by SPF-2.3. The letters s,, s, ... S
refer to sets of n subjects. In the type CRF-23 design, each set of subjects
receives only one of the pg treatment combinations. An examination of
part (a) reveals that the design is composed of two completely randomized
designs. Subjects assigned to treatment level a, comprise one type CR-3
design, while subjects assigned to a, comprise the other type CR-3 design.
The building block for the designs shown in parts (b) and (c) is a randomized
block design. In a type RBF-23 design, a single set of subjects (s,) receives
all pg treatment level combinations. By contrast, in a split-plot design
subjects in set s, receive only one level of treatment A but all levels of
treatment B. The analysis of treatments A and B in a split-plot design,
when viewed separately, resembles the analysis for a completely ran-
domized design and a randomized block design, respectively. This analogy
is discussed in Section 8.4.

SPECIAL FEATURES OF
SPLIT-PLOT DESIGNS

Split-plot repeated measures designs in which a subject receives
all levels of some treatments but only one level of other treatments are
sometimes referred to as mixed designs (Lindguist, 1953). Winer (1962)
uses the designation "multifactor experiments having repeated measures
on some elements" for this class of designs.

The origin of the term mixed design as a designation for split-
plot designs can be readily discerned from an inspection of Figure 8.1-le.
In this figure differences between levels a, and a, involve diflerences
between s, and s, as well as the effects of treatment A. However, difierences
between any two levels of treatment B do not involve differences between