Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

368 CHAPTER 12 | Introduction to Analysis of Variance
DEFINITION
The individual conditions or values that make up a factor are called the levels of the
factor.
Like the t tests presented in Chapters 10 and 11, ANOVA can be used with either
an independent-measures or a repeated-measures design. Recall that an independentmeasures
design means that there is a separate group of participants for each of the treatments
(or populations) being compared. In a repeated-measures design, on the other hand,
the same group is tested in all of the different treatment conditions. In addition, ANOVA can
be used to evaluate the results from a research study that involves more than one factor. For
example, a researcher may want to compare two different therapy techniques, examining
their immediate effectiveness as well as the persistence of their effectiveness over time. In
this situation, the research study could involve two different groups of participants, one for
each therapy, and measure each group at several different points in time. The structure of
this design is shown in Figure 12.2. Notice that the study uses two factors, one independentmeasures
factor and one repeated-measures factor:
1. Factor 1: Therapy technique. A separate group is used for each technique (independent
measures).
2. Factor 2: Time. Each group is tested at three different times (repeated measures).
In this case, the ANOVA would evaluate mean differences between the two therapies as well
as mean differences between the scores obtained at different times. A study that combines two
factors, like the one in Figure 12.2, is called a two-factor design or a factorial design.
The ability to combine different factors and to mix different designs within one study
provides researchers with the flexibility to develop studies that address scientific questions
that could not be answered by a single design using a single factor.
Although ANOVA can be used in a wide variety of research situations, this chapter introduces
ANOVA in its simplest form. Specifically, we consider only single-factor designs. That
is, we examine studies that have only one independent variable (or only one quasi-independent
variable). Second, we consider only independent-measures designs; that is, studies that use
FIGURE 12.2
A research design with
two factors. One factor
uses two levels of
therapy technique
(I vs. II) and the second
factor uses three
levels of time (before
after, and 6 months
after). Also notice
that the therapy factor
uses two separate
groups (independent
measures) and the
time factor uses the
same group for all
three levels (repeated
measures).
THERAPY
TECHNIQUE
Therapy I
(Group 1)
Therapy II
(Group 2)
Before
Therapy
Scores for
group 1
measured
before
Therapy I
Scores for
group 2
measured
before
Therapy II
TIME
After
Therapy
Scores for
group 1
measured
after
Therapy I
Scores for
group 2
measured
after
Therapy II
6 Months
After Therapy
Scores for
group 1
measured
6 months after
Therapy I
Scores for
group 2
measured
6 months after
Therapy II