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You have more than two groups and a mean (average) for each ◦ e.g., young = 4.0, ◦ middle aged...

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Hypothesis Tests Related to Differences H0: µ1 = µ2 = µ3 sig. tests p. value =.001 Conditional probability P (Sample Data | Null is True) Level of agreement between Null and sample data DisagreeAgree
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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? 05/26/22 Marketing Research 1
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Page 1: 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.

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

Page 2: 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.

Hypothesis Tests Related to Differences

H0: µ1 = µ2 = µ3

Black Box

sig. tests p. value = .001

Page 3: 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.

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

Page 4: 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.

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?

Page 5: 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.

◦ 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

Page 6: 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.

◦ 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

Page 7: 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.

◦One way ANOVA investigates:◦Main effects factor has an across-the-board effect e.g., age or involvement

05/03/23Marketing Research 7

Page 8: 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.

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

Page 9: 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.

05/03/23Marketing Research 9

No Sex Sex

No Violence 3 4

Violence 3 4

Page 10: 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.

05/03/23Marketing Research 10

2

3

4

5

Low High

No sexSex

VIOLENCE LEVEL

Page 11: 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.

05/03/23Marketing Research 11

No Sex Sex

No Violence 3 3

Violence 4 4

Page 12: 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.

05/03/23Marketing Research 12

2

3

4

5

Low High

No sex

Sex

VIOLENCE LEVEL

Page 13: 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.

◦ 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

Page 14: 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.

05/03/23Marketing Research 14

No Sex Sex

No Violence 3 4

Violence 4 3

Page 15: 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.

05/03/23Marketing Research 15

2

3

4

5

Low High

No sexSex

VIOLENCE LEVEL

Page 16: 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.

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

Page 17: 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.

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.

Page 18: 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.

05/03/23Marketing Research 18


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