
You have more than two groups

and a mean (average) for each
◦ e.g., young = 4.0,
◦ middle aged = 5.0,
◦ older = 4.5

How do you determine the strength of the
covariation?
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◦ Decomposes “variance” into:
 treatment effects
 other factors
 unexplained factors
◦ Compares data to group means
 Subtracts each data point from group mean
 Squares it
 Keeps a running total of “Sum of Squares”
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◦ The Sums of Squares are then:
 Divided by the number of groups
 (To get an estimate “per group”)
 “Mean Squares”
 MSSr = SSr / df
 (variance per group)
 MSSr / MSSu = F
 Total variance “explainable”
◦ F compared to F crit [dfn, dfd]
◦ if F > F crit, difference in population
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◦ One way ANOVA investigates:
◦ Main effects
 factor has an across-the-board effect
 e.g., age
 or involvement
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
Study of movie profits
◦ Dependent variable:
 Gross revenue in dollars [continuous]
◦ Independent variables:
 Sex [categorical]
 Violence
◦ Examine predictors of profitability:
 Sex, violence, interaction (sex * violence)
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5
4
No sex
Sex
3
2
Low
High
VIOLENCE LEVEL
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5
4
No sex
Sex
3
2
Low
VIOLENCE LEVEL
High
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◦ A TWO-WAY ANOVA investigates:
◦ INTERACTIONS
 effect of one factor depends on another factor
 e.g., larger advertising effects for those with no
experience
 importance of price depends on income level and
involvement with the product
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5
4
No sex
Sex
3
2
Low
High
VIOLENCE LEVEL
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
Study of movie profits
◦ Dependent variable:
 Gross revenue in dollars [continuous]
◦ Independent variables:
 Sex [categorical]
 Violence
◦ Examine predictors of profitability:
 Sex, violence, interaction (sex * violence)
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Tests of Between-Subjects Effects
Dependent Variable: Total Gross
Type III Sum
Source
of Squares
Corrected Model
43744.364 a
Intercept
952785.362
SEX
35467.649
VIOLENCE
10228.369
SEX * VIOLENCE
21.589
Error
995088.361
Total
1991539.265
Corrected Total 1038832.725
df
3
1
1
1
1
381
385
384
Mean Square
14581.455
952785.362
35467.649
10228.369
21.589
2611.780
F
5.583
364.803
13.580
3.916
.008
Sig.
.001
.000
.000
.049
.928
a. R Squared = .042 (Adjusted R Squared = .035)
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