The document discusses factorial designs in research, focusing on main effects, interactions, and relevant terminology. It includes examples illustrating the calculation of main effects and how to interpret interactions between independent variables. The document also emphasizes data collection guidelines for conducting factorial studies.

1. Factorial Designs
Brian J. Piper, Ph.D.

2. Goals
• Main Effect(s)
• Interaction
• graph & statistics comparison

3. Terminology
• ceiling effects:
• floor effects:
• factorial design: more than 1 independent variable
–2x3
–3x4
– 2 x 5 mixed (2 between group, 5 within groups)
• factorial matrix (2 x 2) with 4 cells (conditions)
Males Females
Drug 1st 2nd
Placebo 4th 3rd
• main effect: overall effect of an IV (sex or drug)

4. Terminology
• Ceiling effects: mean score near maximum
• Floor effects: mean score near minimum
• factorial design: more than 1 independent variable
–2x3
–3x4
– 2 x 5 mixed (2 between group, 5 within groups)
• factorial matrix (2 x 2) with 4 cells (conditions)
Males (A1) Females (A2)
Drug (B1) 1st 2nd
Placebo (B2) 4th 3rd
• main effect: overall effect of an IV (sex or drug)

5. Main Effect (Intuition)
Main Effect of Type of Training Main Effect of Presentation rate

6. Examining Main Effects
• Main Effects (continued)
– Calculations  row and column means
– For hypothetical data:
• Row mean #1  mean of 17 and 23 (= 20)
• Row mean #2  mean of 12 and 18 (= 15)
• Column mean #1  mean of 17 and 12 (= 14.5)
• Column mean #2  mean of 23 and 18 (= 20.5)

7. Main Effects
• Male and Female college students (N=89)
were assigned to different encoding intervals
(3, 6, 9, 12, or 15) with the Novel Faces and
Places (NFAP) test.
• This design is _____ x _____

8. Main Effects: Intuitive

9. Main Effects: Statistical

10. Main Effects: Statistical
• Between Groups degrees of freedom = #groups - 1

11. More Main Effects
• Attractiveness rating at different times among
bar patrons
Mickey Gilley (1 min): http://www.youtube.com/watch?v=2e2qsnHVAo4&feature=fvst

12. More Main Effects
• Attractiveness rating at different times among
bar patrons
Mickey Gilley (1 min): http://www.youtube.com/watch?v=2e2qsnHVAo4&feature=fvst

13. Interaction
• The effect of one IV (A) depends on the level
of another IV (B)
• Possibilities:
A B AxB
- - -
- - +
+ - -
+ - +
+ + -
- + -
- + +
+ + +

14. Interaction (but no main effect)
Example #1
• Interactions
– IVs  course emphasis and student major
– No main effects (row and column means all equal 75)

15. Guideline
• Parallel Lines: main effect
• Non-parallel lines: interaction

16. Self-Test
• Rats were exposed to MDMA or Saline during
adolescence (age 35 to 60) and locomotor
activity tested at age 65
• Time Main Effect: ?
• Drug Main Effect: ?
• Interaction: ?
Piper et al. (2007) Developmental Psychobiology, 47, 145-157.

17. Example
• Rats were exposed to MDMA or Saline during
adolescence (age 35 to 60) and locomotor
activity tested at age 65
• Time Main Effect: Yes
• Drug Main Effect: No
• Interaction: Yes
Piper et al. (2007) Developmental Psychobiology, 47, 145-157.

18. Emotional Labeling
• Participants (N=32) are asked to label
emotions of faces
Anger Fear
Direct
Averted
Adams & Kleck (2003) Psychological Science, 14, 644-647.

19. Emotional Labeling
• Participants (N=32) are asked to label
emotions of faces
• Response time recorded (ms)
Anger Fear
Direct 862.3 (23.5) 944.5 (27.5)
Averted 914.1 (25.6) 891.2 (24.4)
Adams & Kleck (2003) Psychological Science, 14, 644-647.

20. Guess
• Main effect of direction: ?
• Main effect of expression: ?
• Interaction: ?

21. Guess
• Main effect of direction: No
• Main effect of expression: Yes
• Interaction: ?
Adams & Kleck (2003) Psychological Science, 14, 644-647.

22. Guess
• Main effect of direction: No
• Main effect of expression: Yes
• Interaction: Yes
Adams & Kleck (2003) Psychological Science, 14, 644-647.

23. Statistical Output
Further Factorial Example (12 min): http://www.youtube.com/watch?v=EgVmfryCAkU

24. Decision Times
A Main Effect of Sex:
Main Effect of Type:
Sex x Type Interaction:
Waller & Linn (2012) J Student Research.

25. Decision Times
A
Waller & Linn (2012) J Student Research.

26. A: X axis
B: red versus blue groups

27. Data Collection Guidelines
• Be early
• Be organized
• Pilot (including coding data)
• Be consistent
• Be appreciative
• Be conservative