Information Technology Reference
In-Depth Information
CHAPTER TWELVE
Three-Way Within-Subjects Design
A three-way within-subjects design is one in which the levels of three
within-subjects variables are combined factorially. Given that it is a within-
subjects design, we still require that the participants contribute a data
point to each of the separate cells (each of the unique combinations of the
levels of the independent variables) of the design. The logistics of run-
ning a three-way study can be challenging but, partly because the subjects
are their own controls and partly because each within-subject effect of
interest is associated with its own error term (thus partitioning the total
within-subjects error into separate error components), such a design has
a considerable amount of statistical power. The key is to find appropri-
ate applications of this design that are relatively immune to carry-over
contamination effects.
12.1 A NUMERICAL EXAMPLE OF A THREE-WAY
WITHIN-SUBJECTS DESIGN
The hypothetical data set that will serve as our example uses three time-
independent variables as shown in Figure 12.1. We are engaged in market
research studying the product look of powdered laundry detergent. One
independent variable is the color of the powder: it is colored white, sea
green, or baby blue. The second independent variable is whether or not
the powder contains granules (flecks of bright shiny additions that in
reality contribute nothing to the cleaning power of the detergent). The
third independent variable is the color of the box: It is colored either aqua
or orange.
We will assume that the manufacturer for whom this research is being
conducted is less interested in directly comparing the color of the powder;
thus, we have structured Figure 12.1 to separate the powder color as the
primary break. Within each powder color, we present the results by the
presence or absence of granules and by box color.
Six single heads of households who agreed to participate in the study
are given twelve boxes of detergent corresponding to the twelve cells
(3
12) of the design and a detailed schedule of when to use
each. The schedule randomizes use of these twelve boxes within each
participant as well as between participants. Each time they clean a load
×
2
×
2
=
325
