1. Chapter 8. Experimental Design II: Factorial Designs

2. Chapter 8. Experimental Design II: Factorial Designs Chapter Objectives
Describe factorial designs using a standardized notation system (2x2, 3x5, etc.) and place data accurately into a factorial matrix to calculate row and column means
Understand what is meant by a main, interaction effect and know how to determine if one exists
Identify the varieties of factorials that correspond to the single-factor designs of Chapter 7

3. Chapter Objectives
Identify a mixed factorial design and a PxE factorial
Calculate the number of participants needed to complete each type of factorial design
Construct an ANOVA source table for an independent groups factorial design

4. Factorial Essentials Factorial design = more than one IV
IVs referred to as “factors”
Identifying factorial designs
Notation system
Digits represent IVs
Numerical values of digits represent the # of levels of each IV
2x3 factorial (say: “two by three”)
2 IVs, one with 2 levels, one with 3 = 6 total conditions
2x4x4 factorial
3 IVs, with 2, 4, and 4 levels = 32 total conditions

5. Factorial Essentials Identifying factorial designs Factorial matrix
2x2 (two levels each of type of training and presentation rate)

6. Outcomes—Main Effects and Interactions
Overall effect of IV “type of training”
Main effect compares data in both light-shaded cells (imagery) with data in both dark-shaded cells (rote)
Main effect compares row means (imagery vs. rote)

7. Outcomes—Main Effects and Interactions
Overall effect of IV “presentation rate”
Main effect of compares data in both light-shaded cells (2-sec rate) with data in both dark-shaded cells (4-sec rate)
Main effect compares column means (2-sec vs. 4-sec)

8. Outcomes—Main Effects and Interactions
Calculations  row and column means
For hypothetical data:
Row mean #1 (imagery) = 20
Row mean #2 (rote) = 15
Column mean #1 (2-sec) = 14.5
Column mean #2 (4-sec) = 20.5

9. Outcomes—Main Effects and Interactions
For hypothetical data:
Main effect for type of training
Imagery (M = 20) produces better recall than rote (M = 15)
Main effect for presentation rate
4-sec rate produces better recall (M = 20.5) than 2-sec rate (M = 14.5)

10. Outcomes—Main Effects and Interactions
effect of one factor depends on the level of the other factor, can be described two ways IVs  course emphasis and student major
No main effects (row and column means all equal 75)

11. Outcomes—Main Effects and Interactions
Whether lab or lecture emphasis is better depends on which major is being evaluated
Lab emphasis  science majors do better (80>70)
Lecture emphasis  humanities majors do better (80>70)

12. Outcomes—Main Effects and Interactions
Whether science or humanities majors do better depends on what type of course emphasis there is
Science majors  better with lab emphasis (80>70)
Humanities majors  better with lecture emphasis (80>70)

13. Outcomes—Main Effects and Interactions
Research example 18: Studying in noise or silence
IVs  study conditions (silent or noisy) and test conditions (silent or noisy)
No main effects, but an interaction
Best memory when study and test conditions match

14. Outcomes—Main Effects and Interactions
Interactions can trump main effects
Caffeine, aging, and memory study
Two main effects – neither relevant

15. Outcomes—Main Effects and Interactions
Combinations of main effects and interactions
Main effect for imagery instructions (22>14), no main effect for presentation rate, no interaction

16. Outcomes—Main Effects and Interactions
Combinations of main effects and interactions
No main effect for imagery instructions, a main effect for presentation rate (22>14), no interaction

17. Outcomes—Main Effects and Interactions
Combinations of main effects and interactions
Main effect for imagery instructions (20>16) and presentation rate (20>16), no interaction

18. Outcomes—Main Effects and Interactions
Combinations of main effects and interactions
Interaction and two main effects

19. Outcomes—Main Effects and Interactions
Combinations of main effects and interactions
Interaction and two main effects

20. Outcomes—Main Effects and Interactions
Combinations of main effects and interactions
Line graphs occasionally used to highlight interactions (nonparallel lines indicate interaction)

21. Varieties of Factorial Designs

22. Varieties of Factorial Designs
Mixed factorial designs
At least one IV is a between-subjects factor
At least one IV is a within-subjects factor
Pre-Proactiv
Post-Proactiv
New 12 4 14 11
Old

23. Varieties of Factorial Designs
Factorials with subject and manipulated variables : P x E designs
P = person factor (a subject variable)
E = environmental factor (a manipulated variable)
If E is a repeated measure  mixed P x E factorial
Main effect for P factor
Introverts outperform extroverts, regardless of room size

24. Varieties of Factorial Designs
Factorials with subject and manipulated variables : P x E designs
Main effect for P factor
Introverts outperform extroverts, regardless of room size

25. Varieties of Factorial Designs
Factorials with subject and manipulated variables : P x E designs
Main effect for E factor
Performance worse in small room, regardless of personality

26. Varieties of Factorial Designs
Factorials with subject and manipulated variables : P x E designs
P x E interaction
Introverts do better in large room, while extroverts do better in small room

27. Summary
Factorial designs allow us to evaluate the effects of multiple IVs on the DV or DVs.
There are different types of factorial designs, depending on how you manipulate your IVs.
Between-subjects, repeated measures, mixed, PxE
Main effects of each IV and interactions among IVs are the results from factorial designs.
Factorial ANOVAs are the statistical tests used.
With the experimental design tools at your disposal, remember to be an ethical researcher.