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an aqua box with granules. Third, if blue powder is used, it seems that it
might be best to package it in an orange box with no granules.
In terms of structuring our simple effects tests, it does not appear
critical to directly compare the different powder colors unless further dis-
cussion with the manufacturer indicates that it is called for. As experienced
consultants, we will run a subsequent analysis so that if asked to produce
that information, we will have it available at the time. For the purposes
of our discussion here, we will make our comparisons within each of the
powder colors. Thus, we will want to (a) compare the aqua and orange
box colors for each level of the granules variable for each powder color,
and (b) compare the presence or absence of granules for each level of
box color for each powder color. This strategy will explicitly guide us in
structuring the syntax command structure in SPSS for our simple effects
analyses and in determining which of the paired comparisons will be of
interest in our SAS output.
12.4 THE ERROR TERMS IN A THREE-WAY
WITHIN-SUBJECTS DESIGN
Each of the seven effects of interest is associated with its own error term. As
we saw in Chapter 10, this is always true in a within-subjects design. Each
effect interacts with the subjects effect, and this interaction represents
noise or unpredictability. The most complex effect, for example, is the
three-way interaction; the error term for this effect is the interaction of
subjects with this three-way interaction.
12.5 COMPUTING THE OMNIBUS ANALYSIS BY HAND
As we indicated in Chapter 9, we will not be providing a computational
example of any of the three-way designs (including the present three-
way within-subjects design). However, we do provide the computational
formulas for the three-factor within-subjects design for those students or
instructors who require this level of detail (see Table 12.2).
12.6 PERFORMING THE OMNIBUS ANALYSIS IN SPSS
12.6.1 STRUCTURING THE DATA FILE
The data file for a three-way within-subjects design is structured in an
analogous manner to the data file we used for our two-way example
in Chapter 10. We show in Figure 12.3 the data file for our 2
3
within-subjects design example. The first column, as always, is used for
our participant identification number, and we named this variable
subid
.
The next twelve columns are devoted to the cells representing our three-
way design. We need twelve columns because each column represents a
different combination of the levels of our independent variables and there
are twelve such combinations (2
×
2
×
×
×
=
2
3
12).
