Transcript chapter15 737KB Jan 01 1998 01:35:22 AM

Chapter XV
Chapter XV
Frequency Distribution,
Cross-Tabulation, and
Hypothesis Testing
Chapter Outline
1) Overview
2) Frequency Distribution
3) Statistics Associated with Frequency Distribution
i. Measures of Location
ii. Measures of Variability
iii. Measures of Shape
4) Introduction to Hypothesis Testing
5) A General Procedure for Hypothesis Testing
6) Cross-Tabulations
i. Two Variable Case
ii. Three Variable Case
iii. General Comments on Cross-Tabulations
7) Statistics Associated with Cross-Tabulation
i. Chi-Square
ii. Phi Correlation Coefficient
iii. Contingency Coefficient
iv. Cramer’s V
v. Lambda Coefficient
vi. Other Statistics
8) Cross-Tabulation in Practice
9) Hypothesis Testing Related to Differences
10) Parametric Tests
i. One Sample
ii. Two Independent Samples
iii. Paired Samples
11) Non-parametric Tests
i. One Sample
ii. Two Independent Samples
iii. Paired Samples
12) Internet and Computer Applications
13) Focus on Burke
14) Summary
15) Key Terms and Concepts
16) Acronyms
Internet Usage Data
Table 15.1
RESPONDENT SEX FAMILIARITY INTERNET
NUMBER
USAGE
1
2
3
4
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
1.00
7.00
2.00
2.00
2.00
3.00
2.00
3.00
13.00 7.00
2.00
4.00
2.00
2.00
2.00
3.00
2.00
3.00
1.00
9.00
2.00
4.00
2.00
5.00
1.00
6.00
1.00
6.00
1.00
6.00
2.00
4.00
1.00
6.00
1.00
4.00
1.00
7.00
2.00
6.00
1.00
6.00
1.00
5.00
2.00
3.00
1.00
7.00
2.00
6.00
1.00
6.00
2.00
5.00
2.00
4.00
1.00
4.00
1.00
3.00
14.00
2.00
3.00
3.00
7.00
6.00
2.00
6.00
6.00
15.00
3.00
4.00
9.00
8.00
5.00
3.00
9.00
4.00
14.00
6.00
9.00
5.00
2.00
15.00
6.00
13.00
4.00
2.00
4.00
3.00
ATTITUDE TOWARD USAGE OF INTERNET
Internet Technology Shopping Banking
7.00
3.00
4.00
7.00
6.00
3.00
3.00
5.00
1.00 1.00
5.00
4.00
4.00
5.00
5.00
4.00
6.00
4.00
7.00
6.00
4.00
3.00
6.00
4.00
6.00
5.00
3.00
2.00
5.00
4.00
4.00
3.00
5.00
3.00
5.00
4.00
6.00
6.00
6.00
4.00
4.00
2.00
5.00
4.00
4.00
2.00
6.00
6.00
5.00
6.00
5.00
3.00
5.00
7.00
3.00
6.00
5.00
2.00
3.00
5.00
1.00
2.00
1.00
1.00
1.00
2.00
2.00
2.00
1.00
2.00
2.00
1.00
1.00
2.00
2.00
2.00
2.00
1.00
2.00
1.00
1.00
1.00
2.00
2.00
2.00
2.00
1.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
1.00
2.00
2.00
2.00
1.00
2.00
1.00
2.00
2.00
1.00
2.00
1.00
5
1.00
1.00
1.00
2.00
1.00
1.00
1.00
2.00
1.00
1.00
2.00
2.00
2.00
7.00
Frequency Histogram
Figure 15.1
8
7
Frequency
6
5
4
3
2
1
0
2
3
4
Familiarity
5
6
7
Figure 15.2
Skewness of a Distribution
Symmetric Distribution
Mean
Median
Mode
(a)
Skewed Distribution
Mean Median Mode
(b)
Fig. 15.3
Steps Involved in Hypothesis Testing
Formulate H0 and H1
Select Appropriate Test
Choose Level of Significance, 
Collect Data and Calculate Test Statistic
Determine Probability
Associated with Test
Statistic
Determine Critical
Value of Test Statistic
TSCR
Compare with Level of
Significance,
Determine if TSCR falls
into (Non) Rejection
Region
Reject or Do not Reject H0
Draw Marketing Research Conclusion
Probabilities of Type I & Type II Error
Figure 15.4
95% of
Total Area
 = 0.05
= 15
Z  = 1.645
Critical Value
99% of
of Z
Total Area
Z
 = 0.01
 = 17
Z  = -2.33
Z
Fig. 15.5
Probability of z with a One-Tailed Test
Shaded Area
= 0.9664
Unshaped Area
= 0.0336
0
z = 1.83
A Broad Classification of Hypothesis Tests
Figure 15.6
Hypothesis Tests
Tests of
Differences
Tests of
Association
Distributions
Means
Proportions
Median/
Rankings
Table 15.2
Frequency Distribution of Familiarity
with the Internet
Value label
Not so familiar
Very familiar
Missing
Value
1
2
3
4
5
6
7
9
TOTAL
Valid
Frequency (N) Percentage percentage
0
2
6
6
3
8
4
1
0.0
6.7
20.0
20.0
10.0
26.7
13.3
3.3
0.0
6.9
20.7
20.7
10.3
27.6
13.8
30
100.0
100.0
Cumulative
percentage
0.0
6.9
27.6
48.3
58.6
86.2
100.0
Gender and Internet Usage
Table 15.3
Sex
Internet Usage
Male
Female
Row
Total
Light (1)
5
10
15
Heavy (2)
10
5
15
15
15
Column Total
Internet Usage by Sex
Table 15.4
Sex
Internet Usage
Male
Female
Light
33.3%
66.7%
Heavy
66.7%
33.3%
Column total
100%
100%
Fig. 15.7
Introduction of a Third Variable in
Cross-Tabulation
Original Two Variables
Some Association
between the Two
Variables
No Association
between the Two
Variables
Introduce a Third
Variable
Introduce a Third
Variable
Refined Association
between the Two
Variables
No Association
between the Two
Variables
No Change in
the Initial
Pattern
Some Association
between the Two
Variables
Table 15.5
Sex by Internet Usage
Internet Usage
Sex
Light
Heavy
Total
Male
33.3%
66.7%
100.0%
Female
66.7%
33.3%
100.0%
Table 15.6
Purchase of Fashion Clothing by
Marital Status
Purchase of
Fashion
Clothing
Current Marital Status
Married
Unmarried
High
31%
52%
Low
69%
48%
Column
100%
100%
700
300
Number of
respondents
Table 15.7
Purchase of Fashion Clothing by
Marital Status
Pur chase of
Fashion
Clothing
Sex
Male
Marr ied
Female
High
35%
Unmarried
Not
Mar r ied
40%
Mar r ied
Low
65%
60%
75%
40%
Column
totals
Number of
cases
100%
100%
100%
100%
400
120
300
180
25%
Unmarried
Not
Mar r ied
60%
Table 15.8
Ownership of Expensive
Automobiles by Education Level
Own Expensive
Automobile
Education
College Degr ee
No College Degr ee
Yes
32%
21%
No
68%
79%
Column totals
100%
100%
250
750
Number of cases
Table 15.9
Ownership of Expensive Automobiles
by Education Level and Income Levels
Own
Expensive
Automobile
Low Income
College
Degr ee
Income
High Income
Yes
20%
No
College
Degr ee
20%
College
Degr ee
40%
No
College
Degr ee
40%
No
80%
80%
60%
60%
Column
totals
Number of
r espondents
100%
100%
100%
100%
100
700
150
50
Table 15.10
Desire to Travel Abroad by Age
Desir e to Tr avel Abr oad
Age
Less than 45
45 or Mor e
Yes
50%
50%
No
50%
50%
Column totals
100%
100%
500
500
Number of respondents
Table 15.11
Desire to Travel Abroad
by Age and Sex
Desir e to
Tr avel
Abr oad
Sex
Male
Age
Female
Age
< 45
>=45
<45
>=45
Yes
60%
40%
35%
65%
No
40%
60%
65%
35%
Column
totals
Number of
Cases
100%
100%
100%
100%
300
300
200
200
Table 15.12
Eating Frequently in Fast Food
Restaurants by Family Size
Eat Fr equently in Fast
Food Restaurants
Family Size
Small
Lar ge
Yes
65%
65%
No
35%
35%
Column totals
100%
100%
500
500
Number of cases
Figure 15.8
Chi-Square Distribution
Do Not Reject
H0
Reject H0
Critical
Value
2
A Classification of Hypothesis Testing
Procedures for Examining Differences
Fig. 15.9
Hypothesis Tests
Non-parametric Tests
(Nonmetric Tests)
Parametric Tests
(Metric Tests)
One Sample
* t test
* Z test
Two or More
Samples
Independent
Samples
* Two-Group
t test
* Z test
Paired
Samples
* Paired
t test
One Sample
* Chi-Square
* K-S
* Runs
* Binomial
Two or More
Samples
Independent
Samples
* Chi-Square
* Mann-Whitney
* Median
* K-S
Paired
Samples
* Sign
* Wilcoxon
* McNemar
* Chi-Square
Table 15.13
Eating Frequently in Fast Food
Restaurants by Family Size & Income
Eat
Fr equently
in Fast Food
Restaurants
Low
Family size
Income
High
Family size
Small
Large
Small
Lar ge
Yes
65%
65%
65%
65%
No
35%
35%
35%
35%
Column
totals
Number of
Respondents
100%
100%
100%
100%
250
250
250
250
Table 15.14
Two Independent-Samples t Tests
Summary Statistics
Male
Female
Number
of Cas es
Mean
Standard
Deviation
15
15
9.333
3.867
1.137
0.435
F Test for Equality of Variances
F
value
2-tail
probability
15. 507
.000
t Test
Equal Variances As s umed
t
value
- 4.492
Degrees of
2-tail
freedom probability
28
. 000
Equal Variances Not As sumed
t
value
-4.492
Degrees of
2-tail
freedom probability
18.014
.000
Paired-Samples t Test
Table 15.15
Variable
Number
of Cases
30
30
Internet Attitude
Technology Attitude
Mean
Standard
Deviation
Standard
Error
5.167
4.100
1.234
1.398
.225
.255
Difference = Internet - Technology
Difference
Mean
Standard
deviation
1.067
0.828
Standard
2-tail
error
Correlation prob.
.1511
.809
.000
t
value
Degrees of
freedom
2-tail
probability
7.059
29
.000
Table 15.16
K-S One-Sample Test for
Normality For Internet Usage
Test Distribution - Normal
Mean:
Standard Deviation:
Cases:
6.600
4.296
30
Most Extreme Differences
Absolute
Positive
Negative
.222
.222
- .142
K-S z
1.217
2-Tailed p
.103
Table 15.17
Mann-Whitney U - Wilcoxon Rank
Sum W Test
Internet Usage by Sex
Sex
Mean Rank
Cases
20.93
10.07
15
15
Male
Female
Total
30
U
31.000
W
151.000
z
Corrected for ties
2-tailed p
-3.406
.001
Note
U = Mann-Whitney test statistic
W = Wilcoxon W Statistic
z = U transformed into a normally distributed z statistic.
Wilcoxon Matched-Pairs
Signed-Rank Test
Internet With Technology
Table 15.18
(Technology -
Internet) Cases
-Ranks
23
+Ranks
1
Ties
6
Total
30
z = -4.207
Mean rank
12.72
7.50
2-tailed p = .0000
Table 15.19
Sample
A Summary of Hypothesis Tests
Related to Differences
Application
Level of Scaling
Test/Comments
One sample
Distributions
Nonmetric
K-S and chi-square for
goodness of fit
Runs test for randomness
Binomial test for goodness of
fit for dichotomous variables
One sample
Means
Metric
t test, if variance is unknown
z test, if variance is known
One Sample
Proportions
Metric
z test
One Sample
Contd.
Table 15.19 Contd.
Two Independent Samples
Two independent samples
Distributions
Nonmetric
K-S two-sample test for examining the
equivalence of two distributions
Two independent samples
Means
Metric
Two-group t test
F test for equality of variances
Two independent samples
Proportions
Metric
Nonmetric
z test
Chi-square test
Two independent samples
Rankings/Medians
Nonmetric
Mann-Whitney U test is more
powerful than the median test
Paired samples
Means
Metric
Paired t test
Paired samples
Proportions
Nonmetric
McNemar test for binary variables
Chi-square test
Paired samples
test
Rankings/Medians
Nonmetric
Wilcoxon matched-pairs ranked-signs
is more powerful than the sign test
Paired Samples
RIP15.1
International Brand Equity - The
Name Of The Game
In the 90s, the trend is toward global marketing. How can marketers
market a brand abroad where there exists diverse historical and
cultural differences. According to Bob Kroll, the former president of
Del Monte International, uniform packaging may be an asset, yet,
catering to individual countries' culinary taste preferences is more
important. One recent survey on international product marketing
makes this clear. Marketing executives now believe it's best to think
globally but act locally. Respondents included 100 brand and product
managers and marketing people from some of the nation's largest
food, pharmaceutical, and personal product companies. 39% said
that it would not be a good idea to use uniform packaging in foreign
markets while 38% were in favor of it. Those in favor of regionally
targeted packaging, however, mentioned the desirability of
maintaining as much brand equity and package consistency as
possible from market to market.
RIP15.1 Contd.
But they also believed it was necessary to tailor the package to fit the
linguistic and regulatory needs of different markets. Based on this
finding, a suitable research question can be: Do consumers in
different countries prefer to buy global name brands with different
packaging customized to suit their local needs? Based on this
research question, one can frame a hypothesis that other things being
constant, standardized branding with customized packaging for a
well established name brand will result in greater market share. The
hypotheses may be formulated as follows:
H0: Standardized branding with customized packaging for a well
established name brand will not lead to greater market share in the
international market.
H1: Other factors remaining equal, standardized branding with
customized packaging for a well established name brand will lead to
greater market share in the international market.
RIP15.1 Contd.
To test the null hypothesis, a well established brand like Colgate
toothpaste which has followed a mixed strategy can be selected.
The market share in countries with standardized branding and
standardized packaging can be compared with market share in
countries with standardized branding and customized packaging,
after controlling for the effect of other factors. A two independent
samples t test can be used.
RIP15.2
Statistics Describe Distrust
Descriptive statistics indicate that the public perception of
ethics in business, and thus ethics in marketing, are poor. In
a poll conducted by Business Week, 46% of those surveyed
said that the ethical standards of business executives are
only fair. A Time magazine survey revealed that 76% of
Americans felt that business managers (and thus
researchers) lacked ethics and this lack contributes to the
decline of moral standards in the U.S. However, the general
public is not alone in its disparagement of business ethics.
In a Touche Ross survey of businesspersons, results showed
that the general feeling was that ethics were a serious
concern and media portrayal of the lack of ethics in
business has not been exaggerated.