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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
Factor B
Level 1 Level 2
Level 1
Level 2
Level 3
condition condition condition
condition condition condition
Types of Factorial Designs
• between subjects• within subjects• mixed
Between Subjects
B
1
2
A1 2
Subjects1-10
Subjects11-20
Subjects31-40
Subjects21-30
Within Subjects
B
1
2
A1 2
Subjects1-40
Subjects1-40
Subjects1-40
Subjects1-40
Mixed (A Between, B Within)
B
1
2
A1 2
Subjects1-20
Subjects1-20
Subjects21-40
Subjects21-40
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 2x33x4How many i.v.’s?How many d.v.’s?How many conditions?
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
Therapy
1 2
1
2
40 60
60 40
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.
A
B
1 2
1
2
40 40
60 60
40
60
50 50
A
B
1 2
1
2
3
20
30
20
30
50
60
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.
A
B
1 2
1
2
40 60
60 80
+20
+20
A
B
1 2
1
2
40 60
60 100
+20
+40
A
B
1 2
1
2
3
20
30
20
30
50
90
Drug
Therapy
1 2
1
2
40 60
60 40
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