Three-Way Within-Subjects Design - Analysis of Variance Designs - page 341

Tests of Between-Subjects Effects

This is the between
subjects variance ( SS S )
representing individual
differences. SPSS does
not compute an F ratio
for this source.

Measure: MEASURE_1
Transformed Variable: Average

Type III Sum
of Squares

Source
Intercept
Error

df Mean Square F Sig.

1003.520
4.958

1003.520
.992

1
5

1011.953 .000

Figure 12.15 Summary table for between-subjects effect.

There are seven effects of interest: the three main effects, the three
two-way interactions, and the three-way interaction. Each is evaluated by
its own error term. As we noted in Table 12.1, all of the effects except the
main effect of boxcolor are significant.
Figure 12.15 shows the between-subjects portion of the variance. The
Intercept concerns the full model, which we do not deal with here. What
SPSS calls Error is the variance representing individual differences; it does
not calculate an F ratio for this effect.

12.8 PERFORMING THE POST-ANOVA ANALYSIS IN SPSS

Configure the analysis as you did for the omnibus ANOVA but at the
end of the process click the Paste pushbutton instead of clicking OK .The
underlying syntax will then be placed in a syntax window; locate that
window on your desktop and make it active by clicking it. This window is
shown in Figure 12.16.
With a significant three-way interaction we need to perform our tests
of simple effects. These should be based on the way we finally chose to
graphically present the interaction in Figure 12.2. In that plot, we separated
the bars into three groupings based on the color of the powder as the most
global split (the variable that increments most slowly), presence or absence
of the granules as the next most global split (the variable that increments
next most slowly), and the box color as the most rapidly incrementing
variable. In the set of variables enclosed by parentheses following the
/EMMEANS TABLES subcommand, powcolor therefore should be

listed first, granules should be listed next, and boxcolor should be in the
rightmost position.
Within each color of powder, some comparisons of the cell means
are desirable. We therefore should type in two compare additions to the
syntax, one comparing granules and another comparing boxcolor .This
is shown in Figure 12.17.
Because the main effect of powcolor is so strong an effect and because
it has three levels, it would be useful to perform a paired comparison of
the means for this effect as well. This can be done in syntax using compare
specifications on the /EMMEANS

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TABLES subcommand for the main
effect as shown as well in Figure 12.17. After entering the necessary syntax,
select Run ➜ All from the main menu to perform the analysis.

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