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To grasp the idea of an interaction, we need to separately examine the
pattern of the means for each level of one of the independent variables.
It is easiest to describe the strategy we would use for gender because
in Figure 8.3 we have drawn separate lines for females and males. We
observe the pattern for females: loneliness steadily increases as we look at
those who reside in large cities, small towns, and rural communities. That
pattern is noticeably different for the male respondents. Loneliness scores
are higher for those residing in small towns compared to large cities and
rural communities.
Such a difference in pattern - such unique standing of the cell means in
the design - as we see in Figure 8.3 is indicative of an interaction. Had the
lines been parallel, there would be no difference between the two patterns
and there would be no interaction. That is, each cell mean for males would
have stood in the same relationship to the other cell means for males as
the matching cell mean stood with respect to the other female cell means.
Note that the lines need not cross for there to be an interaction - it is
quite sufficient for them to be nonparallel for a statistically significant
interaction to be obtained.
8.5.2 SIMPLE EFFECTS ANALYSIS
An interaction is an overall assessment of the relationship of the cell means.
Just as main effects with three or more levels of the independent variable
are omnibus effects that need to be further explicated by post hoc tests
or planned comparisons, so too must the omnibus interaction effect be
simplified. The need for this simplification process can be illustrated by
examining the plot in Figure 8.3.
Consider the female participants. The curve steadily rises from large
city residence to rural communities, but it would be of interest to deter-
mine if, for example, those in small towns are significantly lonelier than
those in large cities or if those living in rural communities are significantly
lonelier than those living in small towns.
For males, it is likely (although we do not know for sure at this stage)
that those living in rural communities are significantly less lonely than
those living in small towns. We also do not currently know if there is a
statistically significant difference between those living in large cities and
those living in small towns, nor can we tell if there is a statistically signifi-
cant difference between those living in large cities and those living in rural
communities.
The same ambiguity is encountered if we look at the gender compar-
isons in Figure 8.3. Is the female-male difference statistically significant
for those residing in large cities? The difference is minimal and is not likely
to be significant. Is there a gender difference for those residing in rural
communities? That difference is relatively large and is probably signifi-
cant. How about female-male differences in small towns? The answer to
that cannot be determined from the graph.
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