Transcript Slides-3-14-07

BA 275
Quantitative Business Methods
Agenda
 Analyzing Survey Data

Chi-square Test of Independence


Contingency Tables
Chi-square Test of a Contingency Table
 Download PRACTICE FINAL from the class
website.
1
Final Examination
 Tuesday, 3/20/2007 from 4:00 – 5:50 p.m.
 Room: GLFN Auditorium
 Check the seating chart when you arrive. You must sit in the
assigned seat to receive your own exam booklet.
 Topics: Comprehensive





Regression analysis accounts for 50%.
Need a calculator that works and a good night sleep.
The normal, t and c2 tables (Tables A, D, and F) will be provided.
A 4” x 6” index card is allowed.
Additional office hours during the finals week
 Monday, 3/19/2007, 1:00 – 3:00 p.m.
 Tuesday, 3/20/2007, 9:00 – 11:00 a.m.
 Tuesday, 3/20/2007, 1:00 – 3:30 p.m.
2
Analyzing Categorical Data
 Do you own an iPod? ___Yes ___No
 Do you own a XBoX? ___Yes ___No
 Which of the following 4 soft drinks gives you
the highest satisfaction?




Type A ___
Type B ___
Type C ___
Type D ___
 Your gender: ____Male ____ Female
 Your nationality: _____
3
Contingency Table

XBOX
No XBOX
Total
iPod
75
15
90
No iPod
45
165
210
Total
120
180
300
Define







Event E as student selected who owns an iPod, and
Event F as student selected who owns a XBOX.
What is P(E), the proportion of students who have iPods? What is P(F), the
proportion of students who have XBOXs?
What is P(E and F), the proportion of students who have both iPods and XBOX?
Events E and F are mutually exclusive if they cannot both occur. That is, P(E and
F) = 0.
What is P(E | F), the proportion of students with XBOXs who also have iPods?
Events E and F are independent if the presence or absence of E does not affect
the probability of F. That is, P(E | F) = P(E).
4
Chi-square Test
Nationality
American
Canadian
Mexican
TOTAL
A
72
26
7
105
Cola Preference
B
C
8
12
10
16
10
14
28
42
D
23
33
19
75
TOTAL
115
85
50
250
H0: The two classifications are independent
Ha: The two classifications are dependent
What is the marketing implication?
5
Observed vs. Expected Counts
Nationality
American
Canadian
Mexican
TOTAL
OBSERVED COUNTS (Oij)
Cola Preference
A
B
C
72
8
12
26
10
16
7
10
14
105
28
42
D
23
33
19
75
TOTAL
115
85
50
250
EXPECTED COUNTS (ASSUME INDEPENDENCE) (eij)
Cola Preference
Nationality
A
B
C
D
TOTAL
American
48.30
12.88
19.32
34.50
115
Canadian
35.70
9.52
14.28
25.50
85
Mexican
21.00
5.60
8.40
15.00
50
TOTAL
105.00
28.00
42
75
250
6
Two Similar or Different Tables?
Nationality
American
Canadian
Mexican
TOTAL
OBSERVED COUNTS (Oij)
Cola Preference
A
B
C
72
8
12
26
10
16
7
10
14
105
28
42
D
23
33
19
75
TOTAL
115
85
50
250
EXPECTED COUNTS (ASSUME INDEPENDENCE) (eij)
Cola Preference
Nationality
A
B
C
D
TOTAL
American
48.30
12.88
19.32
34.50
115
Canadian
35.70
9.52
14.28
25.50
85
Mexican
21.00
5.60
8.40
15.00
50
TOTAL
105.00
28.00
42
75
250
7
Chi-square Statistic – a measure of
similarity/difference
Nationality
American
Canadian
Mexican
TOTAL
OBSERVED COUNTS (Oij)
Cola Preference
A
B
C
72
8
12
26
10
16
7
10
14
105
28
42
D
23
33
19
75
TOTAL
115
85
50
250
EXPECTED COUNTS (ASSUME INDEPENDENCE) (eij)
Cola Preference
Nationality
A
B
C
D
TOTAL
American
48.30
12.88
19.32
34.50
115
Canadian
35.70
9.52
14.28
25.50
85
Mexican
21.00
5.60
8.40
15.00
50
TOTAL
105.00
28.00
42
75
250
r
c
c  
2
i 1 j 1
O
ij
 eij

2
eij
2
2
2
72  48.3
8  12.88
19  15






Large or small?
Implication?
48.3
 42.75
12.88
15
8
Chi-square Statistic
c
Cutoff
2
Degrees of freedom = (#rows – 1 ) x (#cols – 1)
If c  c
2
2
Tables look different
Reject H0
Two classifications are DEPENDENT.
If c  c
2
2
Tables look similar
Do not reject H0
Two classifications are INdependent.
9
Critical Values of c2
10
Example 1
1. Many insurance companies are beginning to question the policy of offering reduced rates to
owners of subcompact cars because the companies claim that their rate of serious and fatal
accidents is higher than that of owners of larger-sized cars. To investigate this issue, a researcher
made an analysis of accident data to determine the distribution of numbers of cases in which at
least one individual was either fatally or critically injured for automobiles of three sizes. The
data for 346 accidents are shown below. Do the data indicate that the frequency of fatal and
critical injuries in auto accidents depends on the size of automobiles? Use =0.05.
Expected counts are printed below observed counts
Size of Auto
Result
Subcompact
Compact
Full Size
Fatal/critical
67
26
16
injury
61.43
28.04
19.53
No fatal/critical
128
63
46
injury
133.57
60.96
42.47
ChiSq = 0.505 + 0.148 + 0.639 + 0.232 + 0.068 + 0.294 = 1.886
11
Example 2
2. Applied marketing research is intended as a support activity for the marketing manager since
information from research can be a key factor in the marketing decision-making process. The
extent to which research influences marketing management, however, is heavily dependent on
how marketing managers view marketing research. A recent survey of marketing managers in
four different industries provided the data in the following table, which gives the managers’
attitudes toward marketing research and its value in marketing decision making. Do the data
present sufficient evidence to indicate that the perceived value of marketing research differs
among marketing managers in the four industries involved in the study? Use =0.05.
Expected counts are printed below observed counts
Industry Type
Perceived
Consumer
Industrial
Retail and
Finance and
Value of
Firms
Organizations
Wholesale
Insurance
Market
Research
Little value
9
22
13
9
14.56
20.70
5.69
12.06
Moderate
29
41
6
17
value
25.55
36.32
9.98
21.15
Great value
26
28
6
27
23.90
33.98
9.33
19.79
TOTAL
64
91
25
53
ChiSq = 2.122 + 0.082 + 9.405 + 0.775 + 0.467 + 0.603 + 1.586
+ 0.816 + 0.185 + 1.052 + 1.191 + 2.627 = 20.911
12
Finally ….
13