Linear Statistical Models
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Answering the questions you
have asked.
• Are these ratings really different?
• What is the influence of a policy variable
(price, advertising, and etc.) on a market
outcome (market shares, sales, overall
satisfaction)?
• What is the part worth of a particular feature
in a whole bundle that makes a product?
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Are these ratings really different?
• Comparing one mean to a null hypothesis
– One Sample t-test
• Comparing two samples means to each
other
– Two Sample t-test
• What about comparing six mean ratings
– Why not 6*5/2 = 15 paired t-tests?
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Degrees of freedom
• We are asking if a series of 6 mean ratings
are really all the same (the variations around
the mean are just noise).
• We shouldn’t run 15 paired t-tests with only
5 independent pieces of information. A
complex pattern of redundancy will make
the results deceptive.
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Community Survey
I. Goods and Services
PLEASE RATE all of the following using the scale below.
-------->
-------->
-------->
-------->
-------->
Really Need
1
Need
2
Indifferent
3
Don’t Need
4
Really Don’t Need
5
1. What goods or services are MOST needed in your neighborhood? (Please circle one
for each type)
Fast Food Restaurants
Sit-down Restaurants
Clothing Stores
Copying/Faxing
Banking
Postal
Other (please specify)________________
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1
1
1
1
1
1
2
2
2
2
2
2
2
3
3
3
3
3
3
3
4
4
4
4
4
4
4
5
Need for Fast-Food Facilities
Need for Sit-Down Restaurants
40
Frequency
Frequency
15
10
5
30
20
10
0
0
1
2
3
Really Need = 1
4
5
1
Really Don't Need = 5
2
Really Need = 1
3
4
5
Really Don't Need = 5
Need for a Copy /Fax Store
Need for a Clothing Store
Frequency
20
15
10
5
1
2
3
Really Need = 1
4
5
0
1
Really Don't Need = 5
2
Really Need = 1
Need for Banking Facilities
3
4
5
Really Don't Need = 5
Need for a Postal Facility
25
30
20
Frequency
Frequency
Frequency
25
30
25
20
15
10
5
0
20
10
15
10
5
0
1
2
Really Need = 1
3
4
Really Don't Need = 5
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0
1
2
Really Need = 1
3
4
Really Don't Need = 5
5
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What the Community Wants the Most
Really Need = 1
Really Don't Need = 5
3.00
2.50
2.00
1.50
1.00
0.50
0.00
FastFood
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Sit Dow n
Clothing Store
Copy Store
Banking
Postal
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Testing Hypotheses about What
Facilities are Most Needed
• Null hypothesis:
– The different facilities are all equally needed
• Alternative hypothesis:
– Some kind are rated as more needed than others
• Test statistic
– F =Variance Between Groups/Variance Within
– = Signal / Noise
• Decision Rule: Set Alpha at .05
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Anova: Single Factor
SUMMARY
Groups
FastFood
Sit Down
Clothing Store
Copy Store
Banking
Postal
Count
62
69
65
62
67
63
ANOVA
Source of Variation
Between Groups
Within Groups
SS
41.04
645.67
Total
686.71
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Sum
Average Variance
180
2.90
2.22
131
1.90
1.50
133
2.05
1.42
127
2.05
1.19
149
2.22
1.93
149
2.37
1.88
df
5
382
MS
8.21
1.69
F
4.86
P-value
0.0003
F crit
2.24
387
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Once you have found a
significant difference overall
• Post Hoc Comparisons
– You can do as many paired t-tests as you want
without worrying about redundancy.
– You can use advanced test (Range Tests) to see
which ratings stand out.
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