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

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.

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

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

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

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)

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

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

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