FACTORIAL DESIGNS
What is a Factorial Design?
Why are Factorials Useful?
What is a Main Effect?
What is an Interaction?
Examples of Factorial Designs
What is a Factorial Design?
A
design containing two or more
independent variables (factors) with all
combinations of levels of factors measured.
Levels and Conditions
A level is a value of a factor. Each factor
has two or more levels.
 A condition is a combination of levels of
different factors.

Factor A
Level 1
Level 1
Level 2
Level 3
condition
condition
condition
condition
condition
condition
Factor B
Level 2
Types of Factorial Designs



between subjects
within subjects
mixed
Between Subjects
1
A
2
1
Subjects Subjects
1-10
21-30
2
Subjects
11-20
B
Subjects
31-40
Within Subjects
1
A
2
1
Subjects Subjects
1-40
1-40
2
Subjects
1-40
B
Subjects
1-40
Mixed (A Between, B Within)
1
A
2
1
Subjects Subjects
1-20
21-40
2
Subjects
1-20
B
Subjects
21-40
Notation for Factorials
The number of numbers tells you how
many IV’s.
 The numbers tell you how many levels.
 A factorial with two IV’s that each have
two levels is a 2 x 2 factorial.

Notation for Factorials
2x2
How many i.v.’s?
How many d.v.’s?
How many conditions?
2x3
3x4
Why Are Factorials Useful?


Reduce amount of non-systematic variance
Ability to measure interaction
– Many behaviors are affected by interactions
– Main effects can be misleading without
considering the interaction
Drug
1
2
1
40
60
2
60
40
Therapy
What is a Main Effect?
 The
overall effect of one IV, averaging over
the levels of the other IV.
 If the means of the levels (marginal means)
are different, there is a main effect.
 On a graph of means, marginal means can
be estimated visually.
1
A
2
1
40
40
40
2
60
60
60
50
50
B
A
2
1
3
1
20
20
50
2
30
30
60
B
What is an Interaction?
 The
effect of one IV changes depending on
the level of the other IV.
 If the simple effects are different, there is an
interaction.
What is an Interaction?
A
simple effect is the difference in means
between levels of an IV for just one level of
another IV.
 On a graph, non-parallel lines indicate an
interaction.
1
A
2
1
40
60
+20
2
60
80
+20
B
1
A
2
1
40
60
+20
2
60
100
+40
B
A
1
2
3
1
20
20
50
2
30
30
90
B
Drug
1
2
1
40
60
2
60
40
Therapy
Examples of Factorial Designs
Culture, anger, and concessions
(Adam et al. 2010)
Anger, catharsis belief, and desire to play video games
(Bushman & Whitaker , 2010)
Face shape cues , sex, and gaze categorization
(Jones et al., 2010)
Implicit evaluations and relationship decay
(Lee et al., 2010)
Touch and investment
(Levav & Argo, 2010)
Family climate and inflammatory activity
(Miller & Chen , 2010)
Adam H et al. Psychological Science 2010;21:882-889
Copyright © by Association for Psychological Science
Bushman B J , Whitaker J L Psychological Science
2010;21:790-792
Copyright © by Association for Psychological Science
Jones B C et al. Psychological Science 2010;21:796-798
Copyright © by Association for Psychological Science
Lee S et al. Psychological Science 2010;21:857-864
Copyright © by Association for Psychological Science
Levav J , Argo J J Psychological Science 2010;21:804-810
Copyright © by Association for Psychological Science
Miller G E , Chen E Psychological Science 2010;21:848-856
Copyright © by Association for Psychological Science