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CHAPTER SEVENTEEN
Advanced Topics in Analysis of Variance
The purpose of this final chapter is to provide a brief introduction to
some selected topics related to experimental design and ANOVA proce-
dures. These topics include interaction comparisons, random and fixed
factors, nested factors, Latin squares, unequal sample sizes, and multi-
variate analysis of variance. Because complete coverage of these topics
requires at least a separate chapter per topic, which is beyond the scope
of the present topic, our coverage will be somewhat cursory; sources that
may be consulted for further information are provided in connection with
each topic.
17.1 INTERACTION COMPARISONS
17.1.1 SIMPLE EFFECTS ANALYSES
As we indicated in Chapter 8, most researchers explore a statistically
significant
A
B
interaction effect by conducting simple effects analy-
ses. The simple effects strategy that we have used throughout this topic
was to perform pairwise comparisons using
t
tests directly following the
omnibus ANOVA that yielded a statistically significant interaction effect.
An alternative but similar strategy with three or more levels of one of
the independent variables can be illustrated by considering the means
displayed in Figure 17.1. This 3
×
2 factorial was originally presented in
Figure 8.2. In this alternative but similar strategy, we focus on one level
of one of the independent variables at a time. In Figure 17.1 we have out-
lined the means of the females to highlight one focus, and would repeat
this focus with the males. To implement this strategy, we would do the
following:
×
1. Perform a one-way ANOVA for the females comparing the means
of type of residence.
2. If the
F
ratio for type of residence is statistically significant, we
would then perform either planned or unplanned comparisons to
determine the locus of the interaction effect.
3. We would then repeat this procedure for the males.
These two strategies for conducting simple effects analyses, direct pair-
wise
t
tests and one-way ANOVAs followed by multiple comparisons tests,
are conceptually very similar in that they both immediately decompose
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