Chapter XI: Factorial Designs
11.1 Introduction To Factorial Designs
In most research situations, the goal is to examine the relationship between two variables
by isolating those variables within the research study.
The idea is to eliminate or reduce the influence of any outside variables that may disguise
or obscure the specific relationship under navigation.
An experimental research typically focuses on the independent variable (which is expected
to influence behavior) and one dependent variable (which is a measure of the behavior).
The non-experimental and quasi-experimental designs usually investigate the relationship
between one quasi-independent variable and one dependent variable.
Behavior usually is influenced by a variety of different variables acting and interacting
Researchers often design research studies that include more than one independent
variable (or quasi-independent variable).
Recall, that in non-experimental and quasi-experimental research. The variable that
differentiates the groups of participants or the groups of scores is called the quasi-
When two or more independent variables are combined in a single study, the independent
variables are commonly called factors.
A research study involving two or more factors is called a factorial design.
A research study with only one independent variable is often called a single-factor
Factorial designs use a notation system that identifies both the number of factors and the
number of values or levels that exist for each factor.
A 2 2 factorial design is considered the simplest factorial design.
A 2 2 factorial design represents a two-factor design with two levels of the first factor and
two levels of the second, with a total of four treatment conditions.
A 2 3 2 factorial design would represent a three-factor design with two, three, and two
levels of each of the factors, respectively, for a total of 12 conditions.
In an experiment, an independent variable is often called a factor, especially in experiments
that include two or more independent variables.
A research design that includes two or more factors is called a factorial design.
One advantage of a factorial design is that it creates a more realistic situation than can be
obtained by examining a single factor in isolation.
Behavior is influenced by a variety of factors usually acting together.
It is sensible to examine two or more factors simultaneously in a single study.
Combining two or more factors within one study provides researchers with a unique
opportunity to examine how the factors influence behavior and how they influence or
interact with each other.
Combing two variables permits researchers with a unique opportunity to examine how the
factors influence behavior and how they influence or interact with each other.
The idea that two factors can act together, creating unique conditions that are different
from either factor acting alone, underlies the value of a factorial design.
11.2 Main Effects & Interactions
The primary advantage of a factorial design is that it allows researchers to examine how
unique combinations of factors acting together influence behavior.
The structure of a two factor design can be represented by a matrix in which the levels of
one factor determine the columns.
The levels of the second factor determine the rows. Each cell in the matrix corresponds to a specific combination of the factors; that is, a
The research study would involve observing and measuring a group of individuals under
the conditions described by each cell.
The data from a two factor study provides three separate and distinct sets of information
describing how the two factors independently and jointly affect behavior.
The difference among three column means is called the main effect.
For reaction time, smaller numbers indicate faster times.
The differences between the column means define the main effect for one factor, and the
differences between the row means define the main effect for the second factor.
A factorial design allows researchers to examine how combinations of factors working
together affect behavior.
In some situations, the effects of one factor simply add on to the effects of the other factor.
Although the two factors are being applied simultaneously, the result is the same as if one
factor contributed its effect, and then the second factor followed and added its effect.
The two factors are operating independently and neither factor has a direct influence on the
One factor will have a direct influence on the effect of a second factor, producing an
interaction between factors.
When two factors interact, their combined effect is different from the simple sum of the two
The main differences among the levels of one factor are called the main effect of that factor.
When the research study is represented as a matrix with one factor defining the rows and the
second factor defining the columns, then the mean differences among the rows define the main
effect for one factor, and the mean differences among the columns