Factorial Designs 6i5t2f
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COMPLEX EXPERIMENTAL DESIGNS
© 2009 The McGraw-Hill Companies, Inc.
Factorial Designs: Designs with more than one independent variable (or factor) Simplest Factorial Design
2 x 2 factorial design Has two independent variables Each independent variable has two levels
© 2009 The McGraw-Hill Companies, Inc.
2 X 2: type of therapy by type of spider 4 conditions DV: score of spider phobia scale – higher the less afraid Therapy Exposure only
Type of spider
Exposure + Cognitive
Type of spider means:
Real spider
6
9
7.5
Fake spider
4
4
4
Therapy means:
5
6.5
© 2009 The McGraw-Hill Companies, Inc.
Interpretation of Factorial Designs
Main effects of an independent variable
when the levels of one IV differ while ignoring the values of the other IV
Interaction between the independent variables
when the effect of one IV depends on the level of the other IV
© 2009 The McGraw-Hill Companies, Inc.
Interpretation of Factorial Designs
Main effects of an independent variable Interaction between the independent variables Therapy Exposure only
Type of spider
Exposure + Cognitive
Type of spider means:
Real spider
6
9
7.5
Fake spider
4
4
4
Therapy means:
5
6.5
Main effect of type of spider
Interaction
Main effect of therapy © 2009 The McGraw-Hill Companies, Inc.
© 2009 The McGraw-Hill Companies, Inc.
© 2009 The McGraw-Hill Companies, Inc.
© 2009 The McGraw-Hill Companies, Inc.
Plot only cell means Use bar graphs when the IV is categorical
Use line graphs when the IV is quantitative © 2009 The McGraw-Hill Companies, Inc.
Factorial Designs with Manipulated and Non-manipulated Variables
IV x PV designs
(Independent Variable by Participant Variable) Therapy
Exposure only gender
Exposure + Cognitive
Gender means:
Men
6
9
7.5
Women
4
4
4
Therapy means:
5
6.5 © 2009 The McGraw-Hill Companies, Inc.
Outcomes of a 2 x 2 Factorial Design
1.
2.
3.
There may be a significant main effect for independent variable A There may be a significant main effect for independent variable B There may be a significant interaction between the independent variables (See results in following slides)
© 2009 The McGraw-Hill Companies, Inc.
© 2009 The McGraw-Hill Companies, Inc.
© 2009 The McGraw-Hill Companies, Inc.
© 2009 The McGraw-Hill Companies, Inc.
© 2009 The McGraw-Hill Companies, Inc.
© 2009 The McGraw-Hill Companies, Inc.
© 2009 The McGraw-Hill Companies, Inc.
Simple main effect of type of therapy at each type of spider Therapy Exposure only
Type of spider
Exposure + Cognitive
Type of spider means:
Real spider
6
9
7.5
Fake spider
4
4
4
Therapy means:
5
6.5
© 2009 The McGraw-Hill Companies, Inc.
Simple main effect of type of spider at each type of therapy Therapy Exposure only
Type of spider
Exposure + Cognitive
Type of spider means:
Real spider
6
9
7.5
Fake spider
4
4
4
Therapy means:
5
6.5
© 2009 The McGraw-Hill Companies, Inc.
Interactions and Simple Main Effects
Simple main effect of type of therapy at each type of spider
© 2009 The McGraw-Hill Companies, Inc.
Interactions and Simple Main Effects
Simple main effect of type of therapy at each type of spider Simple main effect of type of spider at each type of therapy
vs vs
© 2009 The McGraw-Hill Companies, Inc.
Assignment Procedures and Factorial Designs
Independent groups design
Repeated measures design
Participants are only in one level of an IV Participants are in all levels of an IV
Mixed factorial design using combined assignment
One IV is independent, the other is repeated © 2009 The McGraw-Hill Companies, Inc.
© 2009 The McGraw-Hill Companies, Inc.
© 2009 The McGraw-Hill Companies, Inc.
Factorial Designs: Designs with more than one independent variable (or factor) Simplest Factorial Design
2 x 2 factorial design Has two independent variables Each independent variable has two levels
© 2009 The McGraw-Hill Companies, Inc.
2 X 2: type of therapy by type of spider 4 conditions DV: score of spider phobia scale – higher the less afraid Therapy Exposure only
Type of spider
Exposure + Cognitive
Type of spider means:
Real spider
6
9
7.5
Fake spider
4
4
4
Therapy means:
5
6.5
© 2009 The McGraw-Hill Companies, Inc.
Interpretation of Factorial Designs
Main effects of an independent variable
when the levels of one IV differ while ignoring the values of the other IV
Interaction between the independent variables
when the effect of one IV depends on the level of the other IV
© 2009 The McGraw-Hill Companies, Inc.
Interpretation of Factorial Designs
Main effects of an independent variable Interaction between the independent variables Therapy Exposure only
Type of spider
Exposure + Cognitive
Type of spider means:
Real spider
6
9
7.5
Fake spider
4
4
4
Therapy means:
5
6.5
Main effect of type of spider
Interaction
Main effect of therapy © 2009 The McGraw-Hill Companies, Inc.
© 2009 The McGraw-Hill Companies, Inc.
© 2009 The McGraw-Hill Companies, Inc.
© 2009 The McGraw-Hill Companies, Inc.
Plot only cell means Use bar graphs when the IV is categorical
Use line graphs when the IV is quantitative © 2009 The McGraw-Hill Companies, Inc.
Factorial Designs with Manipulated and Non-manipulated Variables
IV x PV designs
(Independent Variable by Participant Variable) Therapy
Exposure only gender
Exposure + Cognitive
Gender means:
Men
6
9
7.5
Women
4
4
4
Therapy means:
5
6.5 © 2009 The McGraw-Hill Companies, Inc.
Outcomes of a 2 x 2 Factorial Design
1.
2.
3.
There may be a significant main effect for independent variable A There may be a significant main effect for independent variable B There may be a significant interaction between the independent variables (See results in following slides)
© 2009 The McGraw-Hill Companies, Inc.
© 2009 The McGraw-Hill Companies, Inc.
© 2009 The McGraw-Hill Companies, Inc.
© 2009 The McGraw-Hill Companies, Inc.
© 2009 The McGraw-Hill Companies, Inc.
© 2009 The McGraw-Hill Companies, Inc.
© 2009 The McGraw-Hill Companies, Inc.
Simple main effect of type of therapy at each type of spider Therapy Exposure only
Type of spider
Exposure + Cognitive
Type of spider means:
Real spider
6
9
7.5
Fake spider
4
4
4
Therapy means:
5
6.5
© 2009 The McGraw-Hill Companies, Inc.
Simple main effect of type of spider at each type of therapy Therapy Exposure only
Type of spider
Exposure + Cognitive
Type of spider means:
Real spider
6
9
7.5
Fake spider
4
4
4
Therapy means:
5
6.5
© 2009 The McGraw-Hill Companies, Inc.
Interactions and Simple Main Effects
Simple main effect of type of therapy at each type of spider
© 2009 The McGraw-Hill Companies, Inc.
Interactions and Simple Main Effects
Simple main effect of type of therapy at each type of spider Simple main effect of type of spider at each type of therapy
vs vs
© 2009 The McGraw-Hill Companies, Inc.
Assignment Procedures and Factorial Designs
Independent groups design
Repeated measures design
Participants are only in one level of an IV Participants are in all levels of an IV
Mixed factorial design using combined assignment
One IV is independent, the other is repeated © 2009 The McGraw-Hill Companies, Inc.
© 2009 The McGraw-Hill Companies, Inc.
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