Be able to identify the factors and levels of each factor from a description
of an experiment

Determine whether a factor is a between-subjects or a within-subjects
factor

Define factorial design

There are many types of experimental designs that
can be analyzed by ANOVA. This section discusses many of these
designs and defines several key terms used.

Factors and Levels

The section on variables defined an independent
variable as a variable manipulated by the experimenter. In
the case study "Smiles
and Leniency," the effect of different types of smiles on
the leniency shown to a person was investigated. Four different
types of smiles (neutral, false, felt, and miserable)
were shown. In this experiment, "Type of Smile" is
the independent variable. In describing an ANOVA design, the term factor is
a synonym of independent variable. Therefore, "Type
of Smile" is the factor in this experiment. Since four types
of smiles were compared, the factor "Type of Smile" has
four levels.

An ANOVA conducted on a design in which there is only one factor is called a one-way ANOVA. If an experiment has two factors, then the ANOVA is called a two-way ANOVA. For example, suppose an experiment on the effects of age and gender on reading speed were conducted using three age groups (8 years, 10 years, and 12 years) and the two genders (male and female). The factors would be age and gender. Age would have three levels and gender would have two levels.

Between- and Within-Subjects Factors

In the "Smiles
and Leniency" study, the four levels of the factor "Type
of Smile" were represented by four separate groups of subjects.
When different subjects are used for the levels of a factor,
the factor is called a between-subjects factor or
a between-subjects variable.
The term "between subjects" reflects the fact that comparisons
are between different groups of subjects.

In the "ADHD
Treatment" study, every subject was tested
with each of four dosage levels
(0, 0.15, 0.30, 0.60 mg/kg) of a drug. Therefore there was only
one group of subjects, and comparisons were not between different
groups of subjects but between conditions within the same subjects.
When the same subjects are used for the levels of a factor,
the factor is called a within-subjects factor or a within-subjects
variable. Within-subjects variables are sometimes referred
to as repeated-measures variables since
there are repeated measurements of the same subjects.

Multi-Factor Designs

It is common for designs to have more than one
factor. For example, consider a hypothetical study of the effects
of age and gender on reading speed in which males and females
from the age levels of 8 years, 10 years, and 12 years are tested.
There would be a total of six different groups as shown in Table
1.

Table 1. Gender x Age Design.

Group

Gender

Age

1

Female

8

2

Female

10

3

Female

12

4

Male

8

5

Male

10

6

Male

12

This design has two factors: age and
gender. Age has three levels and gender has two levels. When all
combinations of the levels are included (as they are here), the
design is called a factorial design.
A concise way of describing this design is as a Gender (2) x Age
(3) factorial design where the numbers in parentheses indicate
the number of levels. Complex designs frequently have more than
two factors and may have combinations of between- and within-subjects
factors.