Information Technology Reference
In-Depth Information
B
B
b
1
b
2
b
1
b
2
b
3
a
1
a
1
A
A
a
2
a
2
a.
A 2x2 design
b.
A 2x3 design
B
b
1
b
2
b
3
b
4
B
a
1
a
2
b
1
b
2
b
3
b
4
b
5
a
1
A
A
a
3
a
2
c.
A 3x4 design
d.
A 2x5 design
Figure 8.1
Illustration of several factorial designs.
The answer to both of these questions is that we can obtain much
more information from conceptualizing it as a two-way design without
losing any information available in the one-way designs that compose it.
Thatis,wecanstilllookatgendermeandifferencesaswewouldina
one-way design with gender as the independent variable and we can still
look at city of residence differences as we would with residence as the
independent variable. But what we gain in treating the study as a two-
way design is the ability to assess the
interaction
of the two independent
variables. This interaction effect reflects the possible differential effects of
the unique combinations of the levels of the independent variables, and
we can evaluate this effect only when we have identified the independent
variables within the context of a factorial design. We will discuss this
interaction effect in greater detail later in this chapter.
8.1.3 CONFIGURING THE TWO-WAY DESIGN
Using generic labels (
A
and
B
) for the names of the independent variables,
we show several different two-way designs in Figure 8.1. It is common
fortwo-waydesignstobedrawninarow
column matrix form as we
have done in the figure. The rows contain the levels of variable
A
and the
columns contain the levels of variable
B
.
Figure 8.1A is a 2
×
”isreadastheword
by
)in
that we have two levels of
A
(
a
1
and
a
2
) and two levels of
B
(
b
1
and
b
2
).
Generally, we designate the design in terms of (the number of levels of
A
)
×
2design(wherethe“
×
×
(the number of levels of
B
). Thus, Figure 8.1B depicts a 2
×
3 design, Fig-
ure 8.1C depicts a 3
×
4 design, and Figure 8.1D depicts a 2
×
5 design.
8.2 A NUMERICAL EXAMPLE
We will illustrate the general principles of a two-way between-subjects
design with a simplified hypothetical example data set. Assume that we
