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The eta squared values are shown in the last column of the summary
table. As we did in Chapter 14, we based these computations on the
separate (sub)total variances of the between-subjects and within-subjects
partitions. Thus, we have computed the eta squared values as follows:
Main effect of
B
:
SS
B
÷
SS
Within Subjects
Interaction
A
×
C
:
SS
A
×
C
÷
SS
Within Subjects
Interaction
A
×
B
×
C
:
SS
A
×
B
×
C
÷
SS
Within Subjects
The plot of the interaction is shown in Figure 15.3. We will narrate
these results once we have performed the simple effects analyses.
15.3 COMPUTING THE OMNIBUS COMPLEXMIXED DESIGN
BY HAND
As we have done with previous three-factor designs in this topic, we
will provide you, the reader, with the necessary computational formulas
should you choose to do these analyses by hand (see Table 15.2).
From our previous discussions within this chapter, the present complex
mixed design has the following sources of between-subjects variance: main
effects of Factor
A
, which is evaluated with the following error term,
S
A
.
Conversely, the within-subjects component is more complex and consists
of the main effect of Factor
B
and the interaction effect of
A
/
×
B
,both
of which are evaluated with the
B
×
S
/
A
error term. Likewise, the main
effect of Factor
C
and the
A
×
C
interaction effect are evaluated by the
C
×
S
/
A
error term. Finally, the
B
×
C
and the
A
×
B
×
C
interaction
effectsareevaluatedwiththe
B
A
error term. Further discussion
of this topic can be found in Keppel (1991) and Keppel and Wickens
(2004).
×
C
×
S
/
15.4 PERFORMING THE OMNIBUS ANALYSIS IN SPSS
15.4.1 STRUCTURING THE DATA FILE
The data file for our three-way, complex mixed design example is shown
in Figure 15.4. The first column, as always, is used for our participant
identification number; we have named this variable
subid
. The next two
columns represent our between-subjects variable of
gender
with females
coded as 1 and males as 2. The last four variables represent the combi-
nations of the within-subjects variables. In the data file, the variable that
increments most rapidly is
toytype
. That is, the third and fourth columns
both relate to yellow toys; the third column, named
yelhand
,representsthe
yellow hands-on toys and the fourth column, named
yelpret
,represents
the yellow pretend toys. Columns five and six both relate to the blue toys;
bluhand
represents the blue hands-on toys and
blupret
represents the blue
pretend toys. In each of these last four columns, the value of the dependent
variable (the number of seconds playing with the toys) is recorded.
