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SECTION 8.1 DESCRIPTION OF DESIGN

s, and s, because the same subjects are observed under all levels of B.
In a type SPF-2.3 design, the main effects of treatment A are said to be
completely confounded with differences between blocks or sets of subjects.
The main effects of B and the interaction AB are free from such confounding.
A confounding scheme in which a treatment is confounded with blocks does
not affect the interpretability of the treatment effects, only the precision of
the estimate. The effects of treatment A are described as between-block
(subject) effects, while the effects of treatment B and interaction AB are
described as within-block (subject) effects. Tests on B and AB are generally
much more powerful than tests on A.

The general designation for a two-factor repeated-measures split-
plot design is SPF-p.g. According to this designation all lower-case letters
before the dot stand for the number of levels of between-block treatments;
letters after the dot stand for levels of within-block treatments.

There are many research problems in the behavioral sciences where
split-plot designs are especially appropriate. A general problem inherent in
all behavioral research is subject heterogeneity. Differences among subjects
are often such as to obscure treatment effects. A repeated measures or
matched subjects design offers the advantage of controlling subject hetero-
geneity. In addition to this advantage, a repeated measures design is
particularly useful in assessing certain types of treatment effects. For
example, in experiments designed to investigate learning, transfer, fatigue,
and so on, the use of repeated measures on the same subjects is often the
simplest way to investigate the research problem. Randomization of the
order-of-treatment level presentation for these kinds of variables is not
always feasible, for the nature of the treatment dictates the order.

A LIMITATION OF THE
USE OF REPEATED MEASURES

A word of caution concerning the use of repeated measurements on
the same subject is in order. When matched subjects are assigned to
within-block treatment levels, it may be assumed that estimates of treat-
ment effects that have been obtained from the g cells are correlated. The
model underlying type SPF-p.g designs permits a particular kind of statis-
tical dependency between observations in the g levels of B but reguires
that the error portion of these scores must be independent of each other
and the treatment effects. There is ample reason to believe that in repeated
measures experiments the error components of the scores are not indepen-
dent and that the variance-covariance matrix departs from the reguired
form. That is, the g x g repeated measures dispersion matrix does not
have all diagonal elements egual to o? and all off-diagonal elements
egual to po?. Procedures for investigating this issue are presented in
Section 8.5. Bargmann (1957) presents a comprehensive discussion of
homogeneity assumptions in repeated measures designs. Lana and Lubin

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