Analysis of Variance Designs
Introduction to ANOVA
- 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
- 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 many 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 showed to a person was investigated. Four different
types of smiles (neutral, false, felt, miserable, on leniency)
were investigated. In this experiment, "Type of Smile" is
the independent variable. In describing an ANOVA design, the term factor is
used as 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
An ANOVA conducted on a
design in which there is only one factor is called a one-way
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 (10 yr, 15 yr, and 20 yr) and the two
genders (males and females). The factors would be age and gender.
Age would have three levels and gender would have two levels.
Between- and Within-Subject 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 the 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 the factor,
the factor is called a within-subjects factor or within-subjects
variable. Within-subjects variables are sometimes referred
to as repeated-measures variables since
there are repeated measurements of the same subjects.
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 were tested.
There would be a total of six different groups as shown in Table
|Table 1. Gender x Age Design
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-subject