# Factorial Designs Passer Chapter 9

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Factorial Designs Passer Chapter 9
Slides Prepared by Alison L. O’Malley

Factorial designs include two or more independent variables
What does it mean for a design to be “crossed”?

Describing Factorial Designs
In a between-subjects factorial design, each participant experiences only one condition In a within-subjects factorial design, each participant experiences every condition Mixed-factorial designs include one or more between-subjects variables and one or more within-subjects variables

Describing Factorial Designs
“two by four by three” Order of variables can be reversed, so long as numbers match up Note how quickly the number of participants required can skyrocket! Need at least three levels to examine nonlinear effects in an IV

Factorial Designs Establish whether variables have a main effect
IV has significant effect on DV (i.e., there is an overall mean difference) Establish interaction effect Effect of IV on DV depends on level of another IV

Interaction Note how the effect of Factor A on the DV
depends on the level of Factor B

Interaction Factor B is a moderator variable

Person x Situation Factorial Design
At least one subject variable along with at least one manipulated situational variable Using gender as a subject variable and room temperature as a manipulated situational variable, develop a 2 x 2 design and a 2 x 3 design How might the conclusions we draw here differ from those based on a research design with two or more manipulated IVs?

More on Main Effects and Interactions
Cell means Marginal means reflect the average of cell means for the relevant row or column

More on Main Effects and Interactions
Is there a main effect of number of witnesses?

More on Main Effects and Interactions
Is there a main effect of number of witnesses? No.

More on Main Effects and Interactions
Is there a main effect of witness-suspect relationship?

More on Main Effects and Interactions
Is there a main effect of witness-suspect relationship? Yes.

More on Main Effects and Interactions
Is there a number of witnesses x witness- suspect relationship interaction?

More on Main Effects and Interactions
Is there a number of witnesses x witness- suspect relationship interaction? No. Why not?

Graphical Depiction of Results

How would you graph this?

Check your work. This form of interaction is a disordinal
(or crossover) interaction.

Another Example This form of interaction is an ordinal interaction.

Main Effects and Interactions
What does it mean for an interaction to “qualify” a main effect? Do interactions always qualify main effects? What do interactions have to do with the external validity of researchers’ findings?

Analyzing the Results ANOVA is the statistical framework for factorial designs A 2 x 2 ANOVA entails three tests of statistical significance One test for the main effect of Factor A Another test for the main effect of Factor B A test for the A x B interaction

Analyzing the Results In order to make sense of interactions, researchers look at simple main effects The effect of one IV at a particular level of another IV For gender, we would examine three simple main effects

Analyzing the Results If statistically significant simple main effects emerge, simple contrasts are performed (a type of post-hoc test) E.g., Compare men’s performance between different pairs of temperatures

Analyzing the Results A priori theorizing can drive hypotheses about specific mean differences Test with planned comparisons Mean differences need not be as large to be statistically significant

Three IVs Four possible interactions
Three two-way interactions (A x B, A x C, B x C) One three-way interaction (A x B x C)

Three IVs Overall, how many tests of statistical significance
would there be in a 2 x 2 x 2?