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PSY 2005
Week 10 – Simple Effects
Factorial Analysis of Variance
Simple Effects
Aims
• Interpretation of interactions• To explain, using example data, how an analysis of
simple effects allows an interpretation of potential main effects when an interaction is present.
Learning Outcomes
• Interpret graphical representations of interactions
• Define simple effects.• Explain the steps in an analysis of simple effects.• Interpret the results of a simple effects analysis.
At the end of this lecture you will be able to :
Definitions
• 2-way ANOVA– 2 independent variables (IVs)
• Main Effect– The effects of one independent variable (factor)
summed (averaged) over all levels of the other independent variable.
• Interaction– When the effect of one factor is not constant
across all levels of the other factors.
Example
• Effect of music and alcohol on driving performance
• IV 1: Music– On vs. Off
• IV 2: Alcohol– None vs 2 units
• DV: Mean no. of errors made
off on
IV1: Music
DV
: m
ean
no
of e
rror
s
Possible Outcomes
• No main effects• No interaction
2units
no alcohol
IV2: Alcohol
• Main effect for factor1• No main effect for factor 2• No interaction
off on
IV1: Music
DV
: m
ean
no
of e
rror
s
2units
no alcohol
IV2: Alcohol
Possible Outcomes
• No main effect for factor1• Main effect for factor 2• No interaction
off on
IV1: Music
DV
: m
ean
no
of e
rror
s
2units
no alcohol
IV2: Alcohol
Possible Outcomes
• Main effect for factor1• Main effect for factor 2• No interaction
off on
IV1: Music
DV
: m
ean
no
of e
rror
s
2units
no alcohol
IV2: Alcohol
Possible Outcomes
• No main effects• Interaction
off on
IV1: Music
DV
: m
ean
no
of e
rror
s
2units
no alcohol
IV2: Alcohol
Possible Outcomes
• Main effect for factor1• Main effect for factor 2• Interaction
off on
IV1: Music
DV
: m
ean
no
of e
rror
s
2units
no alcohol
IV2: Alcohol
Possible Outcomes
Example Data
A B C
Drug
24
57
24
11
31
33
3x 6x 3x
1x 2x 3x
x
4
2
x 2 4 3 3x
depression
Schizo-phrenia
Factor 1
Factor 2
Drug A
Type of Drug
Schizophrenics
DepressivesMean improvement score
Drug CDrug B
Interaction Graph
Interpreting Interactions
• In order to interpret any potential main effects, an analysis of Simple Effects should be conducted.
• A Simple Effect is the effect of one independent variable at a particular level of the other independent variable.
• For our example there are two simple effects for type of drug and three simple effects for type of problem.
• In order for a main effect to be interpretable, the simple effects for that variable must be the same for all levels of the other independent variable.
Simple Effects for Type of Drug
• There are two simple effects for type of drug:
1. the effect of drug for schizophrenics2. the effect of drug for depressives
1. the effect of drug for schizophrenics
Conduct a one-way independent groups ANOVA, using the MSerror from the original two-way ANOVA and appropriate degrees of freedom, to assess if there is any difference between the scores of the three drugs for schizophrenics only.
2. the effect of drug for depressives
Conduct a one-way independent groups ANOVA, using the MSerror from the original two-way ANOVA and appropriate degrees of freedom, to assess if there is any difference between the scores of the three drugs for depressives only.
If the effect of drug is the same for schizophrenics and depressives then there is an interpretable main effect for drug.
Is there?
The question we are addressing here is:Is the effect for drug consistent (the same) for schizophrenics and depressives?
Simple Effects for Type of Problem
• There are three simple effects for type of problem:
1. the effect of type of problem for Drug A2. the effect of type of problem for Drug B3. the effect of type of problem for Drug C
1. the effect of type of problem for Drug A
Conduct a one-way independent groups ANOVA, using the MSerror from the original two-way ANOVA and appropriate degrees of freedom, to assess if there is any difference between the scores of the participants for Drug A only.
2. the effect of type of problem for Drug B
Conduct a one-way independent groups ANOVA, using the MSerror from the original two-way ANOVA and appropriate degrees of freedom, to assess if there is any difference between the scores of the participants for Drug B only.
3. the effect of type of problem for Drug C
Conduct a one-way independent groups ANOVA, using the MSerror from the original two-way ANOVA and appropriate degrees of freedom, to assess if there is any difference between the scores of the participants for Drug C only.
If differences between schizophrenics and depressives are in the same direction for all three types of drug then there is an interpretable main effect for type of problem.
Is there?
The question we are addressing here is:
Is the effect for type of problem consistent (the same) for all three types of drug?