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

SECTION 12.1 | Introduction (An Overview of Analysis of Variance) 367
Population 1
(Treatment 1)
Population 2
(Treatment 2)
Population 3
(Treatment 3)
m 1
= ?
m 2
= ?
m 3
= ?
FIGURE 12.1
A typical situation in
which ANOVA would
be used. Three separate
samples are obtained to
evaluate the mean differences
among three populations
(or treatments)
with unknown means.
Sample 1
n 5 15
M 5 23.1
SS 5 114
Sample 2
n 5 15
M 5 28.5
SS 5 130
Sample 3
n 5 15
M 5 20.8
SS 5 101
enough evidence to conclude that there are mean differences among the three populations.
Specifically, we must decide between two interpretations:
1. There really are no differences between the populations (or treatments). The
observed differences between the sample means are caused by random, unsystematic
factors (sampling error) that differentiate one sample from another.
2. The populations (or treatments) really do have different means, and these population
mean differences are responsible for causing systematic differences between
the sample means.
You should recognize that these two interpretations correspond to the two hypotheses (null
and alternative) that are part of the general hypothesis-testing procedure.
■ Terminology in Analysis of Variance
Before we continue, it is necessary to introduce some of the terminology that is used to
describe the research situation shown in Figure 12.1. Recall (from Chapter 1) that when a
researcher manipulates a variable to create the treatment conditions in an experiment, the
variable is called an independent variable. For example, Figure 12.1 could represent a study
examining driving performance under three different telephone conditions: driving with no
phone, talking on a hands-free phone, and talking on a hand-held phone. Note that the three
conditions are created by the researcher. On the other hand, when a researcher uses a nonmanipulated
variable to designate groups, the variable is called a quasi-independent variable.
For example, the three groups in Figure 12.1 could represent 6-year-old, 8-year-old,
and 10-year-old children. In the context of ANOVA, an independent variable or a quasiindependent
variable is called a factor. Thus, Figure 12.1 could represent an experimental
study in which the telephone condition is the factor being evaluated or it could represent a
nonexperimental study in which age is the factor being examined.
DEFINITION
In analysis of variance, the variable (independent or quasi-independent) that
designates the groups being compared is called a factor.
In addition, the individual groups or treatment conditions that are used to make up a
factor are called the levels of the factor. For example, a study that examined performance
under three different telephone conditions would have three levels of the factor.