
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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7/17/2016
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Hypothesis Tests Related to Differences
Black Box
H0: µ1 = µ2 = µ3
sig. tests
p. value = .001
Hypothesis Tests Related to Differences
.001
Disagree
H0: µ1 = µ2 = µ3
1.0
Agree
Conditional probability
P (Sample Data | Null is True)
Level of agreement between
Null and sample data
sig. tests
p. value = .001
Hypothesis Tests Related to Differences
Looking
atanything
the(or
averages
for
each
box
size
(u1,
u2,
u3),
Hmmm,
isisthere
else
that
westores),
might
like
to know
about
each
Consider
the
potential
sales
volume
of
three
different
of the
Okay,
With
sothe
What
the
variance
same
about
in
the
sales
lack
variance?
of)
(across
difference
Let’s
occurring
look
are
and
the
three
see.
insizes
the
different
next
set
What
about
Lets
get
this
rid
third
of
the
set
“Black
of
comparisons?
Box”
do we
believe
that
these
3
types
sell
the
same?
group
of
sales cereal.
data?or why not?
same
Cheerios
comparisons
ofthe
comparison?
same?
Why
u1
u2
u3
sig. tests
p. value = .001
H0: µ1 = µ2 = µ3
u1
u2
u3
u1
u2
u3
◦ 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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7/17/2016
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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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7/17/2016
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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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7/17/2016
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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)
Marketing Research
7/17/2016
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No Sex
Sex
No Violence
3
4
Violence
3
4
Marketing Research
7/17/2016
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5
4
No sex
Sex
3
2
Low
High
VIOLENCE LEVEL
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7/17/2016
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No Sex
Sex
No Violence
3
3
Violence
4
4
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5
4
No sex
Sex
3
2
Low
VIOLENCE LEVEL
High
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7/17/2016
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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
Marketing Research
7/17/2016
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No Sex
Sex
No Violence
3
4
Violence
4
3
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5
4
No sex
Sex
3
2
Low
High
VIOLENCE LEVEL
Marketing Research
7/17/2016
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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)
Marketing Research
7/17/2016
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◦ Interpret the results
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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7/17/2016
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