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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?
05/03/23Marketing Research 1
Hypothesis Tests Related to Differences
H0: µ1 = µ2 = µ3
Black Box
sig. tests p. value = .001
Hypothesis Tests Related to Differences
H0: µ1 = µ2 = µ3 sig. tests
p. value = .001
Conditional probabilityP (Sample Data | Null is True)
Level of agreement betweenNull and sample data
Disagree Agree.001 1.0
Lets get rid of the “Black Box”
Hypothesis Tests Related to Differences
H0: µ1 = µ2 = µ3
Consider the potential sales volume of three different sizes of the same Cheerios cereal.
sig. tests p. value = .001
u1 u2 u3
u1 u2 u3
u1 u2 u3
Looking at the averages for each box size (u1, u2, u3), do we believe that these 3 types sell the same?
Okay, so is the same (or lack of) difference occurring in the next set of comparison?
What about this third set of comparisons? Hmmm, is there anything else that we might like to know about each
group of sales data? What about the variance? Let’s look and see. With the variance in sales (across stores), are the three different
comparisons the same? Why or why not?
◦ 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”
05/03/23Marketing Research 5
◦ 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
05/03/23Marketing Research 6
◦One way ANOVA investigates:◦Main effects factor has an across-the-board effect e.g., age or involvement
05/03/23Marketing Research 7
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)
05/03/23Marketing Research 8
05/03/23Marketing Research 9
No Sex Sex
No Violence 3 4
Violence 3 4
05/03/23Marketing Research 10
2
3
4
5
Low High
No sexSex
VIOLENCE LEVEL
05/03/23Marketing Research 11
No Sex Sex
No Violence 3 3
Violence 4 4
05/03/23Marketing Research 12
2
3
4
5
Low High
No sex
Sex
VIOLENCE LEVEL
◦ 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
05/03/23Marketing Research 13
05/03/23Marketing Research 14
No Sex Sex
No Violence 3 4
Violence 4 3
05/03/23Marketing Research 15
2
3
4
5
Low High
No sexSex
VIOLENCE LEVEL
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)
05/03/23Marketing Research 16
05/03/23Marketing Research 17
◦ Interpret the resultsTests of Between-Subjects Effects
Dependent Variable: Total Gross
43744.364a 3 14581.455 5.583 .001952785.362 1 952785.362 364.803 .00035467.649 1 35467.649 13.580 .00010228.369 1 10228.369 3.916 .049
21.589 1 21.589 .008 .928995088.361 381 2611.780
1991539.265 3851038832.725 384
SourceCorrected ModelInterceptSEXVIOLENCESEX * VIOLENCEErrorTotalCorrected Total
Type III Sumof Squares df Mean Square F Sig.
R Squared = .042 (Adjusted R Squared = .035)a.
05/03/23Marketing Research 18