Information Technology Reference
In-Depth Information
A
B
C
D
b
1
b
2
b
2
b
2
b
2
b
1
b
1
b
1
a
1
a
1
a
2
Figure 8.4
Examples of interactions: A, B, and C show interactions that likely would
be statistically significant (the functions are not parallel) but D shows an instance where
the interaction would not be significant (the functions are parallel).
a
2
a
1
a
2
a
1
a
2
An analysis of the simple effects for the interaction would answer
all of these questions. The general strategy that we use in generating
the simple effects is to isolate the levels of a variable and compare the
means of those groups. For example, we would isolate the levels of gender.
Doing that, we would focus on female respondents and compare the
groups of different residents (large city, small town, rural community).
We would then do the same for males. Additionally, we could isolate the
different levels of residence and compare females and males in each type
of community. Knowing which group means differ from which others
would permit us to fully explicate the omnibus interaction effect. We
will show you how to perform these simple effects analyses later in the
chapter.
In general, interactions can usually be diagnosed by examining the
plot of the cell means. We have provided schematized plots in Figure
8.4 to illustrate this. The functions in Figure 8.4A, Figure 8.4B, and Fig-
ure 8.4C depart from a parallel relationship and would be indicative of an
interaction.
In Figure 8.4A the function for
b
1
slants slightly down and the
function for
b
2
slants sharply up. It is likely that the two functions
would not differ significantly at
a
2
but would differ significantly
at
a
1
.
In Figure 8.4B, the functions cross. At
a
1
we are likely to find
b
2
of
significantly greater magnitude than
b
1
;at
a
2
, it is possible that
b
1
and
b
2
may not differ significantly.
In Figure 8.4C both functions rise but
b
2
is rising more sharply than
b
1
. It is likely that the two functions do not differ significantly at
a
1
but would be significantly different at
a
2
.
Figure 8.4D pictures the two functions as parallel. This would tell us
in advance of examining the ANOVA summary table that the interaction
effect would not achieve statistical significance.
