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CHAPTER NINE
Three-Way Between-Subjects Design
9.1 A NUMERICAL EXAMPLE OF A THREE-WAY DESIGN
In Chapter 8 we added a second independent variable into a between-
subjects design to generate a two-way factorial. At this point you probably
realize that we are not limited to combining just two between-subjects
independent variables in research designs (although we are still limiting
ourselves to analyzing a single dependent variable). Theoretically, we could
combine many such variables together, despite the fact that the complexi-
ties of such designs grow exponentially as the designs get more complex. It
is possible to see in the research literature some ANOVA designs using five
independent variables and a few using four variables; however, three-way
designs are the common limit for most research questions. If you under-
stand the logic of analyzing a three-way design, you can invoke the same
strategies to handle those with four or five independent variables.
We will illustrate the general principles of a three-way between-subjects
design by using the following simplified hypothetical example data set.
Assume that we wish to measure citizen satisfaction with the public school
system. We sample individuals representing three different political prefer-
ences: liberal, moderate, and conservative (coded 1, 2, and 3, respectively,
in the data file). We also code for whether or not these individuals voted in
last election (yes coded as 1 and no coded as 2), using voting as an indi-
cator of political involvement. Finally, we code for whether or not there
are school-aged children living in the home (yes coded as 1 and no coded
as 2).
To assess satisfaction with the public school system, we administer a
survey to each of the participants and compute a total score. Satisfaction
scores near zero reflect little satisfaction with the system; scores near or
at the maximum of 40 reflect considerable satisfaction with the public
school system. These scores comprise our dependent variable.
The design, together with the data, is presented in Figure 9.1. There
are five participants per cell. Note that with three independent variables,
drawing the configuration in such a way that we can show all of the
data points is not a trivial manner. In order to schematically present the
design, we need to show it in segments by isolating the levels of one of
the independent variables. We have chosen to display the data by separating
the participants on the basis of whether or not school-aged children are
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