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MORE on ANOVA
What is an Error Term?
What is a Mixed ANOVA?
What is a Three-Way ANOVA?
What is a Three-Way Interaction?
Why Should You Be Careful about Higher-Order ANOVAs?
What is an Error Term?
• The denominator of the F-test in any
ANOVA is also called the error term.
• In different types of ANOVA, the error term
is calculated differently.
• The error term always contains only nonsystematic variance.
What is a Mixed ANOVA?
• Factorial ANOVA with at least one
between-subjects factor and at least one
within-subjects factor.
• Dividing the variance becomes more
complicated.
• The F-tests are interpreted in the same way.
What is Three-Way ANOVA?
• Factorial ANOVA with three factors.
• All combinations of levels of all three
factors are measured.
• Can be between subjects, within subjects, or
mixed.
1
A
2
1
B
1
2
1
A
C
2
1
B
2
2
Effects Tested in
a Three-Way ANOVA
•
•
•
•
•
•
•
Main Effect of A
Main Effect of B
Main Effect of C
AxB Two-way Interaction
AxC Two-way Interaction
BxC Two-way Interaction
AxBxC Three-way Interaction
What is a Three-Way
Interaction?
• A two-way interaction that changes
depending on the level of a third factor.
• Example: For inpatients, the effect of the
drug is greater for people getting cognitive
than behavior therapy. For outpatients, the
effect of the drug is greater for people
getting behavior therapy.
Drug
Placebo
Drug
Prozac
Placebo
Prozac
20
40
20
60
20
60
20
40
Inpatient
Outpatient
Setting
Why Should You be Careful
about Higher-Order ANOVAs?
• You must always interpret the most
complex effect that is significant.
• Results of higher-order ANOVAs become
difficult to interpret.
• “Never eat anything bigger than your
head.”