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model with all three effects combined (added) together. In the context
of ANOVA, we ordinarily wish to obtain the eta squared value for each
separate effect. To do this, as we had to do with SPSS, we must perform
the hand calculation, dividing each sum of squares by the total sum
of squares (
Corrected Total
) shown in Figure 8.29. The coefficient of
variation (the ratio of the standard deviation of the sample as a whole to
the mean of the sample as a whole), the root mean square error, and the
grand mean of the dependent variable are also displayed in that middle
table.
8.15 PERFORMING THE POST-ANOVA ANALYSES IN SAS
The omnibus analysis indicated that all of the effects were statistically
significant. In practice, we would tend not to bother with the main
effects because we have obtained a statistically significant interaction in
the omnibus analysis. However, to illustrate how we would approach the
main effects, we will discuss them here.
Only one main effect can be unambiguously interpreted as it stands -
because there were only two levels of
gender
,fromourdescriptivestatistics
we know that the females felt significantly more loneliness than the males.
Fortheothertwoeffects(themaineffectof
reside
and the interaction),
we need additional information before we can render an interpretation of
the results.
We wish to perform comparisons of the means for (a) the main effect
of
reside
and (b) the means of the groups for the interaction, that is, we
wish to perform tests of simple effects. If we wanted to use a Tukey test
for the main effect and Bonferroni tests for the simple effects, we would
need to perform the analysis twice, once for the Tukey procedure and
again for the Bonferroni procedure. For our purposes, we opt here to use
a Bonferroni corrected multiple comparisons test for both of these so that
we can accomplish the specifications in one step.
Configure the analysis as described above. Then select the
Least
Squares
portion of the
Post Hoc Tests
tab. This brings you to the screen
showninFigure8.30.For
Classeffects touse
,set
reside
and
gender
reside
to
True
; this will generate, respectively, the post hoc tests for the main effect
of
reside
and the simple effects tests for the interaction.
Least squares means are the same values that SPSS calls estimated
marginal means as described in Section 8.9.2. By placing the post hoc tests
in the context of least squares, it makes it clear that these post hoc tests are
performed in the least square means. When working with the estimated
marginal means in SPSS, we performed Bonferroni corrected pairwise
comparisons; for this reason, we will also perform Bonferroni compar-
isons here in
SAS Enterprise Guide
.Thus,for
Comparisons
,set
Show
p-values for differences
to
All pairwise differences
and set
Adjustment
method for comparison
to
Bonferroni
.Thenclick
Run
to perform the
comparisons.
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