1. Experiments with Multiple Independent Variables
Ryan M. Denney, Ph.D.
The University of Southern Mississippi
PSY 361

2. Factorial Design
A factorial design gives us the power to devise an investigation of several independent variables in a single experiment.
“Factors” = IVs
Allows us to look at combinations of IVs at the same time, a situation that is quite similar to the real world.
There are probably few, if any, situations in which behavior is affected by only a single factor (variable) at a time.

3. Factorial Design Example: Factor A: customer hearing (deaf/hearing)
Factor B: Salesclerk sex (male/female)
2X2 Design: 2 factors (IVs) each with 2 levels
DV: the speed at which salesclerks help customers
Randomly assign male/female salesclerks to deaf/hearing groups
hearing
deaf
Deaf customers/female clerks
Hearing customers/female clerks
female
male
Deaf customers/male clerks
Hearing customers/male clerks

4. Factorial Design
Mixed assignment: some levels of the IVs are randomly assigned, while others are not.
In a 2 IV design, one IV is randomly assigned, and one IV is not.
Main effect
The sole effect of one IV in a factorial design.
Example: the solitary effect of customer hearing OR the solitary effect of salesclerk sex
Interaction effect
Joint, simultaneous effect of more than one IV on the DV
The effect of one IV depends on the particular level of another IV
Example: The effect of customer hearing depends on salesclerk sex

5. Interaction Effect
This graph displays effects of the clothing, the effects of the customer sex, and the interaction between clothing and customer sex.

6. Interaction Effect—Con’t
Each point represents the mean of a group
Clothing style and customer sex interacted to affect salesclerks’ response times.
Women received help quickly regardless of their attire, but men received help quickly only if they were not sloppily dressed.
Men attired in sloppy clothes had to wait longer for help than the other three groups (well-dressed men, well-dressed women, sloppily dressed women)

7. Three-Way Factorial Design
A factorial design with three IVs
Example: salesclerk sex, customer hearing, customer sex

8. Analyzing Factorial Designs
Statistical labels reflect the size of the design include:
Factorial ANOVA
Two-way ANOVA
Three-way ANOVA
Instead of having one IV as the sole source of treatment variability, factorial designs have multiple IVs and their interactions as sources of treatment variability.
Example: variability may come from: salesclerk sex, customer hearing and the interaction of these IVs

9. Rationale for Factorial ANOVA (2 IVs)
Allows us to evaluate separately the effects of each of the 2 IVs as well as their interaction