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In-Depth Information
8.6 PRECEDENCE OF EFFECTS: INTERACTIONS SUPERCEDE
MAIN EFFECTS
There is a general rule governing the precedence in which we interpret
and report the results of factorial analyses: Interactions supersede main
effects. This is true because interactions contain a more complete level of
detail than main effects. In our worked example, we obtained a significant
main effect of gender - the overall “gender” means revealed that females
experienced more loneliness than males. But because the interaction was
statistically significant as well, we can see that the main effect is in this
instance an overgeneralization. Yes, females by and large reported more
loneliness than males, but not universally. For those residing in large cities,
male respondents actually reported slightly more loneliness than females.
Although this latter difference may not be statistically significant, the point
is that the generalization based on the main effect does not hold for the
large city environment.
It is further true that while females reported more loneliness than
males in both small towns and rural communities, the magnitude of this
difference is very different. Once again, the generalization based on the
main effect is too broad to capture the nuances of the results.
Because an interaction indicates that the lines are not parallel and that
studying the unique combinations of the cells is critical, it will always be
true that the details of the relationships existent at the cell mean level
will always be more informative regarding the subtleties of the group
differences than the main effects. Thus, with a significant interaction, we
ordinarily spend most of our energy explicating the cell means based on
our simple effects analysis and tend to provide more cursory treatment of
the main effects.
8.7 COMPUTING AN OMNIBUS TWO-FACTOR BETWEEN-
SUBJECTS ANOVA BY HAND
8.7.1 NOTATION
The computational process for a two-factor between-subjects ANOVA is a
direct extension of the computational procedures we covered in Chapter 6
for the single-factor between-subjects ANOVA design. We will continue
with the hypothetical example introduced in this chapter. The indepen-
dent variables are size of residence community (Factor
A
) and gender
(Factor
B
). The residence independent variable has three levels (
a
1
=
large,
a
2
=
small,
a
3
=
rural) and gender has two levels (
b
1
=
female,
b
2
=
male). The dependent variable is a score (from 0 to 60) on a loneli-
ness inventory. This combination of independent variables produces a 3
×
2 factorial and is depicted in the first matrix of Table 8.2, labeled
Design
.
Respondents' scores on the loneliness inventory (dependent variable)
can be arranged into six columns or treatment combinations of the various
levels of the two independent variables. Such an arrangement can be seen
