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Table 10.4.
Comparison matrix for a pairwise within-groups comparison
One month before One year after
Subjects
a
1
a
2
Sum (
S
)
s
1
12
5
17
s
2
9
5
14
s
3
9
6
15
s
4
8
4
12
s
5
8
5
13
s
6
9
7
16
s
7
12
4
16
s
8
6
5
11
Sum (
A
):
73
41
114
Sum of
s
quared scores (
Y
aj
) :
695
217
912
Mean (
Y
j
):
9.13
5.13
7.13
group means. Conducting a set of planned comparisons will allow us to
discover what is “driving” this treatment effect and also will allow us to
directly test specific research hypotheses that we may have formulated at
the start of the study. We encourage the interested reader to review our
previous general discussion of this topic in Chapter 7, Section 7.14.
In the between-subjects designs that we covered previously, analytical
comparisons are evaluated with the omnibus error term (e.g.,
MS
S
/
A
,
MS
S
/
AB
). In the within-subjects case the overall within-subjects error term
(
MS
A
×
S
) is generally not appropriate, particularly if the assumptions of the
analysis have been violated (Keppel et al., 1992; Keppel & Wickens, 2004).
This is because the overall within-subjects error term captures information
from all of the conditions; when we perform planned comparisons, we are
very often focusing on only a subset of the conditions and need an error
term that represents only those conditions. Thus, comparisons should
be made with a separate or unique error term that is based only on the
treatments currently being compared. There are a variety of approaches to
develop these separate error terms, some of which are reviewed in Keppel
and Wickens (2004).
We will demonstrate perhaps the simplest approach to making a
within-subjects comparison offered by Keppel et al. (1992) that produces
a unique error term. Based on our previous numerical example, suppose
we are interested in comparing groups
a
1
(one month before) and
a
5
(one
year after) in order to examine the most extreme preeffects and posteffects
on symptom intensity. The analysis begins by creating what we will call a
Comparison Matrix
based on the two treatment groups we are interested
in, and the necessary
A
and
S
sums (see Table 10.4).
As can be seen, Table 10.4 is a recapitulation of Table 10.2 but with
only two treatment groups. Notice that former treatment group
a
5
is now
designated
a
2
. Thus, we are now poised to recompute our analysis with
