1. Graziano and Raulin Research Methods: Chapter 12
Factorial Designs
Graziano and Raulin
Research Methods: Chapter 12
Graziano & Raulin (2000)
Graziano & Raulin (1997)

2. Factorial Designs Includes two or more independent variables
Essentially two (or more) studies in one
By testing more than one independent variable at a time, we can look at the interactive effects of independent variables
Most independent variables in psychology interact with other independent variables
Graziano & Raulin (2000)

3. Main Effects and Interactions
The effect of each of the independent variables on the dependent variable is the main effect of that variable
The combined effect of two or more independent variables on the dependent variable is an interaction
In complex designs, there may be several main effects and interactions to consider
Graziano & Raulin (2000)

4. Graphing Factorial Designs
For two independent variables (IV)
Select one IV, and label the X-axis with the levels of that IV
Label the Y-axis with enough range to graph the mean scores of each cell
Graph and label the means from the first level of the second IV and label that line
Repeat that process for each level of the second IV, labeling each line
Graziano & Raulin (2000)

5. Sample Data to Graph
Graziano & Raulin (2000)

6. Graph of Previous Slide
Graziano & Raulin (2000)

7. Factorial ANOVA ANOVA can analyze any factorial design
The number of effects will depend on the number of independent variables (IVs)
2 IVs: A & B main effects; AB interaction
3 IVs: A, B, & C main effects; AB, AC, BC, & ABC interactions
4 IVs: A, B, C, & D main effects; AB, AC, AD, BC, BD, CD, ABC, ABD, BCD, & ABCD interactions
5 IVs: You DON’T want to know!
Graziano & Raulin (2000)

8. Repeated-Measures Factorials
Can use a within-subjects (also called repeated measures) design in a factorial study
As with all within-subjects designs, sequence effects must be controlled
The ANOVA will have to take into account that the same participants appear in all of the conditions
Graziano & Raulin (2000)

9. Mixed Designs
The IVs do not have to be the same (e.g., all within-subjects or all between-subjects)
Mixed (within-subjects & between-subjects): the ANOVA must take this into account
Mixed (manipulated & nonmanipulated): will affect the interpretation
Mixed in both senses is also possible
Graziano & Raulin (2000)

10. Variations on ANOVA ANOVA is a flexible analysis approach
Handles any number of IVs and any combination of within-subjects and between-subjects factors
Variations of ANOVA
ANCOVA (Analysis of Covariance)
MANOVA (Multivariate Analysis of Variance)
Easy to do with statistical analyses programs
Graziano & Raulin (2000)

11. Summary Factorial designs are like running two or more studies at once
Factorial studies are the only way to study the interaction of independent variables
ANOVA will analyze factorial studies
Factors may be mixed
within-subjects and between-subjects factors
manipulated and nonmanipulated factors
Graziano & Raulin (2000)