MORE COMPARISONS OF MEANS
• 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?
7/17/2016
Marketing Research
1
ANOVA
– 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”
7/17/2016
Marketing Research
2
ANOVA
– 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
7/17/2016
Marketing Research
3
ANOVA (continued)
– One way ANOVA investigates:
– Main effects
• factor has an across-the-board effect
• e.g., age
• or involvement
7/17/2016
Marketing Research
4
Example
• 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)
7/17/2016
Marketing Research
5
Main effect: Sex
5
4
No sex
Sex
3
2
Low
7/17/2016
High
Marketing Research
6
Main effect: Violence
5
4
No sex
Sex
3
2
Low
7/17/2016
High
Marketing Research
7
ANOVA
– 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
7/17/2016
Marketing Research
8
Interaction: Sex by Violence
5
4
No sex
Sex
3
2
Low
7/17/2016
High
Marketing Research
9
Example
• 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)
7/17/2016
Marketing Research
10
SPSS Output
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
a.
R Squared
7/17/2016
df
3
1
1
1
1
381
385
384
Mean Square
14581.455
952785.362
35467.649
10228.369
21.589
2611.780
= .042 (Adjusted R Squared
.035)
Marketing =
Research
F
5.583
364.803
13.580
3.916
.008
Sig.
.001
.000
.000
.049
.928
11
The End
7/17/2016
Marketing Research
12