More Than One Independent Variable
Laying Out a Factorial Design
A Research Example
Choosing a Between-Subjects Design
What is a factor?
A factor is an independent variable.
More Than One Independent Variable
What is a factorial design?
A factorial design contains more than one
independent variable.
The effect of psychotherapy (IV1) and
antidepressant drugs (IV2) on depression (DV).
A two factor experiment is the simplest factorial
design.
More Than One Independent Variable
What information can a factorial design provide?
A factorial design can provide information
about both treatment and interaction effects.
More Than One Independent Variable
What is a main effect? What determines the number
of main effects in an experiment?
A main effect is the action of a single IV
on the DV.
There can be as many main effects as
independent variables.
More Than One Independent Variable
Provide an example of a main effect in a
hypothetical study of exercise and depression.
An experimenter studies the effects of exercise
intensity (IV1) and duration (IV2) on depression
(DV).
If exercise intensity or duration separately
reduced depression, these would constitute
main effects.
More Than One Independent Variable
How do we determine whether we have main effects
in our experiment?
Perform an appropriate statistical test.
More Than One Independent Variable
In a 2 x 3 x 3 study, how many IVs and treatment
conditions are there?
There are 3 independent variables and 18
treatment conditions.
More Than One Independent Variable
Provide an example of a 2 x 3 x 3 study.
The independent variables were the perpetrator’s
gender (male or female), relationship to the child
(parent, step-parent, or parent’s partner), and
severity of the abuse (neurological damage,
broken bones, or bruising).
The dependent variable was sentence length.
More Than One Independent Variable
What is an interaction?
An interaction is the joint effect of two or more
IVs on the DV.
When there is an interaction, the effect of one
IV is different across levels of the other IV.
More Than One Independent Variable
Provide an example of an interaction.
If the antidepressant Paxil produced greater
reductions in depression in the Cognitive
Behavior Therapy (CBT) condition than the
Waiting List condition, this would illustrate an
interaction between drug and psychotherapy.
More Than One Independent Variable
What is a higher-order interaction?
A higher-order interaction is an interaction
among three or more IVs.
Interpretation can be difficult when more than
three IVs interact in an experiment.
More Than One Independent Variable
Provide an example of a higher-order interaction.
A previous hypothetical study examined the
effect of a perpetrator’s gender (male or female),
relationship to the child (parent, step-parent, or
parent’s partner), and severity of the abuse
(neurological damage, broken bones, or
bruising) on sentencing.
More Than One Independent Variable
Provide an example of a higher-order interaction.
There would be a higher-order interaction if
the perpetrator’s gender, relationship to the child,
and severity of abuse jointly determined
sentence length.
More Than One Independent Variable
How many interactions are possible in a study with
three IVs?
Assign letters (A, B, C) to the independent
variables. Identify all unique two- and threetreatment combinations.
For three independent variables, these include
AB, AC, BC, and ABC. ABC is the higher-order
interaction.
More Than One Independent Variable
How does an interaction affect the interpretation of
our results?
An interaction qualifies a main effect, warning
us that there may be limits or exceptions to the
effect of an IV on the DV.
When there is an interaction, we must consider
both IVs, because the effects of one factor will
depend on the levels of the other factor.
More Than One Independent Variable
Explain the factor-labeling method.
The factor-labeling method lists the two factors
in parentheses after the numerical notation.
For example, 2 x 2 (Type of Name x Length of
Name).
Laying Out a Factorial Design
Explain the factor and levels method.
This method lists the two factors and their
respective levels after the numerical notation.
For example, 2 x 2 (Type of Name: given,
nickname x Length of Name: short, long).
Laying Out a Factorial Design
What advantage does the factor and levels method
have over the factor-labeling method?
The factor and levels method provides more
detailed information about the design than the
factor-labeling method.
Laying Out a Factorial Design
Why use a factorial design instead of two separate
univariate experiments?
A factorial design is more efficient since it
combines several one-factor experiments and
allows us to study interactions.
A factorial design can achieve greater external
validity since it can better recreate the
complexity of the multivariate environment.
A Research Example
Why should we keep between-subjects designs
simple?
Practical limitations include:
 number of subjects
 time
 interpretability of results
Choosing a Between-Subjects Design