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the error term. Eta squared values are determined by dividing the sum of
squares for a statistically significant effect by the sum of squares for the
total variance.
8.4 EFFECTS OF INTEREST IN THIS DESIGN
In this two-way design, there are three effects of interest to us: the main
effect of gender, the main effect of community residence size, and the
unique combinations of the levels of gender and residence known as the
Gender
×
Residence interaction. We look at each in turn.
8.4.1 MAIN EFFECT OF GENDER
One of the effects in which we are interested is that of gender. We want
to know if there was a statistically significant difference in feelings of
loneliness between the female and male respondents. We thus compare
the overall mean of loneliness for females (i.e., across all of the residence
levels) with that of males. As can be seen from Figure 8.2, we are thus
comparing the mean of 31.67 with the mean of 18.00. The ANOVA output
indicates that the F ratio for gender was statistically significant, F (1, 24)
=
2
38
267. With only two levels of gender, we know that
the female respondents experienced significantly more loneliness than the
male respondents.
.
03, p
<.
05,
η
= .
8.4.2 MAIN EFFECT OF RESIDENCE
A second effect in which we are interested is the main effect of residence.
We thus compare the overall means of participants living in large cities,
small towns, and rural communities. It can be seen see from Figure 8.2 that
these means are 15.50, 33.00, and 26.00, respectively. The ANOVA output
shows a statistically significant F ratio for this main effect, F (2, 24)
=
296. We therefore presume that at least one pair of
means differs significantly but do not know precisely which means differ
from which others based on the F ratio information. In this situation,
we would need to conduct a post-ANOVA test (post hoc tests, planned
comparisons) as described in Chapter 7 to determine which group means
differ significantly from which others.
.
<.
η
2
= .
21
06, p
05,
8.4.3 INTERACTION OF THE TWO INDEPENDENT VARIABLES
A third effect that we evaluate in the design is that of the Gender
Res-
idence interaction. Our focus for this effect is on the cell means, that is,
the means representing the unique combinations of the independent vari-
ables. The ANOVA output indicates that we have a statistically significant F
ratio for the interaction effect, F (2, 24)
×
2
269. To
explicate this effect we must examine the relationships of the cell means.
This involves a post-ANOVA procedure known as simple effects analysis.
The interest here is to “simplify” the interaction so that it can be properly
interpreted.
=
19
.
16, p
<.
05,
η
= .
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