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Type of Residence
Large
Small
Rural
Female
15.00
38.00
42.00
Gender
Male
16.00
28.00
10.00
Figure 17.1
Simple effects strategy.
the interaction effect into a direct comparison of means. The use of inter-
action contrasts exemplifies a somewhat different strategy to decompose
the omnibus interaction effect.
17.1.2 INTERACTION CONTRASTS
Interaction components
or
contrasts
examines statistically significant inter-
action effects by decomposing complex factorial designs into a series of
smaller factorial analyses rather than moving directly to a comparison of
means. Such an approach encapsulates the factorial quality of the analysis,
as opposed to the more means-oriented nature of simple effects analyses.
The design displayed in Figure 17.2 illustrates the strategy of per-
forming interaction contrasts. Here we have focused on a subset of the
conditions in the full design by “reducing” or simplifying the full factorial
into a 2
×
2, eliminating (for the moment) the two rural conditions from
the analysis. This smaller factorial arrangement allows us to focus on the
degree of loneliness of females and males and living in large and small
cities.
This
new
A
×
B
interaction
effect
(with
the
reduced
factorial)
addresses a different question than did the original
A
B
interaction.
The original interaction effect asked individuals from large, small, or
rural population centers whether their rated loneliness varied as a func-
tion of gender. The interaction contrast poses a more focused question: Is
the difference in loneliness between large and small population centers the
same for women and men? If the 2
×
×
2 interaction effect was statistically
Type of Residence
Large
Small
Rural
Female
15.00
38.00
42.00
Gender
Male
16.00
28.00
10.00
Large
Small
Female
15.00
38.00
Male
16.00
28.00
Figure 17.2
Interaction contrast strategy.
