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(see Appendix C) at the following degrees of freedom: ( df effect , df S / AB ), at
a particular alpha level. Thus, for the main effect of Factor A ,our F A value
was 21.06 and is evaluated with (2, 24) degrees of freedom. The critical
value of F at these degrees of freedom (at the .05 level) is 3.40. Because
our F A is greater than (or equal to) the critical value, we reject the null
and conclude that size of residential community affects loneliness scores.
Likewise, for the main effect of Factor B ,our F B was 38.04 and is
evaluated with (1, 24) degrees of freedom. The critical value of F is 4.26
at the .05 level. Because our F B is greater than the critical value, we reject
the null and conclude that gender also affects loneliness appraisals.
Lastly, we evaluate the interaction effect ( F A × B =
19.17) with (2, 24)
degrees of freedom. We note that our F A × B is greater than the critical
value of F (3.40); thus, we reject the null and conclude that the two
independent variables (residence and gender) combine to produce a sta-
tistically significant unique joint effect. We will next turn our attention to
the computational details of these statistically significant main effects and
interactions.
8.8 COMPUTING SIMPLE EFFECTS BY HAND
Calculating the simple effects of a two-factor design is comparable to
conducting several single-factor analyses, one at each level of one of the
independent variables. The goal of such analyses is to try and isolate or
identify the source of the statistically significant interaction effect found
in the omnibus analysis. Figure 8.5 depicts the relationship between a
Female (b 1 )
Large
(a 1 )
Small
(a 2 )
Rural
(a 3 )
Large
(a 1 )
Small
(a 2 )
Rural
(a 3 )
Female
(b 1 )
Male
(b 2 )
Male (b 2 )
Rural
(a 3 )
Large
(a 1 )
Small
(a 2 )
Figure 8.5
Relationship of the factorial design to simple effects extraction.
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