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?

04/21/23Marketing 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”

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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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04/21/23Marketing Research 9

No Sex Sex

No Violence 3 4

Violence 3 4

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2

3

4

5

Low High

No sex

Sex

VIOLENCE LEVEL

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No Sex Sex

No Violence 3 3

Violence 4 4

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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

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04/21/23Marketing Research 14

No Sex Sex

No Violence 3 4

Violence 4 3

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2

3

4

5

Low High

No sex

Sex

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)

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◦ Interpret the resultsTests of Between-Subjects Effects

Dependent Variable: Total Gross

43744.364a 3 14581.455 5.583 .001

952785.362 1 952785.362 364.803 .000

35467.649 1 35467.649 13.580 .000

10228.369 1 10228.369 3.916 .049

21.589 1 21.589 .008 .928

995088.361 381 2611.780

1991539.265 385

1038832.725 384

SourceCorrected Model

Intercept

SEX

VIOLENCE

SEX * VIOLENCE

Error

Total

Corrected Total

Type III Sumof Squares df Mean Square F Sig.

R Squared = .042 (Adjusted R Squared = .035)a.

04/21/23Marketing Research 18