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Chapter XVChapter XV
Frequency Distribution, Frequency Distribution, Cross-Tabulation, and Cross-Tabulation, and
Hypothesis TestingHypothesis Testing
Chapter XV
Chapter OutlineChapter Outline
1) Overview1) Overview
2) Frequency Distribution2) Frequency Distribution
3) Statistics Associated with Frequency Distribution3) Statistics Associated with Frequency Distribution
i. Measures of Locationi. Measures of Location
ii. Measures of Variabilityii. Measures of Variability
iii. Measures of Shapeiii. Measures of Shape
4) Introduction to Hypothesis Testing4) Introduction to Hypothesis Testing
5) A General Procedure for Hypothesis Testing5) A General Procedure for Hypothesis Testing
6) Cross-Tabulations6) Cross-Tabulations
i. Two Variable Casei. Two Variable Case
ii. Three Variable Caseii. Three Variable Case
iii. General Comments on Cross-Tabulationsiii. General Comments on Cross-Tabulations
7) Statistics Associated with Cross-Tabulation 7) Statistics Associated with Cross-Tabulation
i. Chi-Squarei. Chi-Square
ii. Phi Correlation Coefficientii. Phi Correlation Coefficient
iii. Contingency Coefficient iii. Contingency Coefficient
iv. Cramer’s Viv. Cramer’s V
v. Lambda Coefficientv. Lambda Coefficient
vi. Other Statisticsvi. Other Statistics
8) Cross-Tabulation in Practice8) Cross-Tabulation in Practice
9) Hypothesis Testing Related to Differences9) Hypothesis Testing Related to Differences
10) Parametric Tests10) Parametric Tests
i. One Samplei. One Sample
ii. Two Independent Samplesii. Two Independent Samples
iii. Paired Samplesiii. Paired Samples
11) Non-parametric Tests 11) Non-parametric Tests
i. One Samplei. One Sample
ii. Two Independent Samplesii. Two Independent Samples
iii. Paired Samplesiii. Paired Samples
12) Internet and Computer Applications12) Internet and Computer Applications
13) Focus on Burke13) Focus on Burke
14) Summary14) Summary
15) Key Terms and Concepts15) Key Terms and Concepts
16) Acronyms16) Acronyms
RESPONDENT SEX FAMILIARITY INTERNET ATTITUDE TOWARD USAGE OF INTERNETNUMBER USAGE Internet Technology Shopping Banking 1 1.00 7.00 14.007.00 6.00 1.001.002 2.00 2.00 2.003.00 3.00 2.002.003 2.00 3.00 3.004.00 3.00 1.002.004 2.00 3.00 3.007.00 5.00 1.002.00 5 1.00 7.00
13.007.00 7.00 1.001.006 2.00 4.00 6.005.00 4.00 1.002.007 2.00 2.00 2.004.00 5.00 2.002.008 2.00 3.00 6.005.00 4.00 2.002.009 2.00 3.00 6.006.00 4.00 1.002.0010 1.00 9.00 15.007.00 6.00 1.002.0011 2.00 4.00 3.004.00 3.00 2.002.0012 2.00 5.00 4.006.00 4.00 2.002.0013 1.00 6.00 9.006.00 5.00 2.001.0014 1.00 6.00 8.003.00 2.00 2.002.0015 1.00 6.00 5.005.00 4.00 1.002.0016 2.00 4.00 3.004.00 3.00 2.002.0017 1.00 6.00 9.005.00 3.00 1.001.0018 1.00 4.00 4.005.00 4.00 1.002.0019 1.00 7.00 14.006.00 6.00 1.001.0020 2.00 6.00 6.006.00 4.00 2.002.0021 1.00 6.00 9.004.00 2.00 2.002.0022 1.00 5.00 5.005.00 4.00 2.001.0023 2.00 3.00 2.004.00 2.00 2.002.0024 1.00 7.00 15.006.00 6.00 1.001.0025 2.00 6.00 6.00 5.00 3.00 1.002.0026 1.00 6.00 13.00 6.00 6.00 1.001.0027 2.00 5.00 4.00 5.00 5.00 1.001.0028 2.00 4.00 2.00 3.00 2.00 2.002.0029 1.00 4.00 4.00 5.00 3.00 1.002.0030 1.00 3.00 3.00 7.00 5.00 1.002.00
Internet Usage DataInternet Usage DataTable 15.1Table 15.1
Frequency HistogramFrequency HistogramFigure 15.1Figure 15.1
2 3 4 5 6 70
7
4
3
2
1
6
5
Fre
qu
ency
Fre
qu
ency
FamiliarityFamiliarity
8
Skewness of a DistributionSkewness of a DistributionFigure 15.2Figure 15.2
Skewed Distribution
Symmetric Distribution
Mean Median Mode
(a)
Mean Median Mode (b)
Formulate H0 and H1
Steps Involved in Hypothesis TestingSteps Involved in Hypothesis TestingFig. 15.3Fig. 15.3
Select Appropriate Test
Collect Data and Calculate Test Statistic
Determine Probability Associated with Test
Statistic
Choose Level of Significance,
Draw Marketing Research Conclusion
Reject or Do not Reject H0
Determine Critical Value of Test Statistic
TSCR
Determine if TSCR falls into (Non)
Rejection Region
Compare with Level of Significance,
Probabilities of Type I & Type II Probabilities of Type I & Type II ErrorError
Figure 15.4Figure 15.4
99% of Total Area
Critical Value of Z
= 15
= 17
= 0.01
= 1.645Z
= -2.33Z
Z
Z
95% of Total Area
= 0.05
Unshaped Area
= 0.0336
Probability of z with a One-Tailed TestProbability of z with a One-Tailed TestFig. 15.5Fig. 15.5
Shaded Area
= 0.9664
z = 1.830
Hypothesis Tests
Distributions
A Broad Classification of Hypothesis TestsA Broad Classification of Hypothesis Tests
Tests of Association
Tests of Differences
Median/ Rankings
Means Proportions
Figure 15.6Figure 15.6
Frequency Distribution of FamiliarityFrequency Distribution of Familiaritywith the Internetwith the Internet
Table 15.2Table 15.2
Valid CumulativeValue label Value Frequency ( N) Percentage percentage percentage
Not so familiar 1 0 0.0 0.0 0.02 2 6.7 6.9 6.93 6 20.0 20.7 27.64 6 20.0 20.7 48.35 3 10.0 10.3 58.66 8 26.7 27.6 86.2
Very familiar 7 4 13.3 13.8 100.0Missing 9 1 3.3
TOTAL 30 100.0 100.0
Gender and Internet UsageGender and Internet UsageTable 15.3Table 15.3
SexRow
Internet Usage Male Female Total
Light (1) 5 10 15
Heavy (2) 10 5 15
Column Total 15 15
Internet Usage by SexInternet Usage by SexTable 15.4Table 15.4
Sex
Internet Usage Male Female
Light 33.3% 66.7%
Heavy 66.7% 33.3%
Column total 100% 100%
Original Two Variables
Introduce a Third Variable
Some Association between the Two
Variables
Introduction of a Third Variable in Introduction of a Third Variable in Cross-TabulationCross-Tabulation
Fig. 15.7Fig. 15.7
Introduce a Third Variable
No Association between the Two
Variables
No Association between the Two
Variables
Some Association between the Two
Variables
Refined Association between the Two
Variables
No Change in the Initial
Pattern
Sex by Internet UsageSex by Internet UsageTable 15.5Table 15.5
Internet Usage
Sex Light Heavy Total
Male 33.3% 66.7% 100.0%
Female 66.7% 33.3% 100.0%
Purchase of Fashion Clothing by Purchase of Fashion Clothing by Marital StatusMarital Status
Table 15.6Table 15.6
Purchase ofFashion
Current Marital Status
Clothing Married Unmarried
High 31% 52%
Low 69% 48%
Column 100% 100%
Number ofrespondents
700 300
Purchase of Fashion Clothing by Purchase of Fashion Clothing by Marital StatusMarital Status
Table 15.7Table 15.7
Purchase ofFashion
SexMale Female
Clothing Marr ied NotMarr ied
Marr ied NotMarr ied
High 35% 40% 25% 60%
Low 65% 60% 75% 40%
Columntotals
100% 100% 100% 100%
Number ofcases
400 120 300 180
Unmarried Unmarried
Ownership of Expensive Ownership of Expensive Automobiles by Education LevelAutomobiles by Education Level
Table 15.8Table 15.8
Own ExpensiveAutomobile
Education
College Degree No College Degree
Yes 32% 21%
No 68% 79%
Column totals 100% 100%
Number of cases 250 750
Ownership of Expensive Automobiles Ownership of Expensive Automobiles by Education Level and Income Levelsby Education Level and Income Levels
Table 15.9Table 15.9
OwnExpensive
IncomeLow Income High Income
Automobile CollegeDegree
NoCollegeDegree
CollegeDegree
NoCollegeDegree
Yes 20% 20% 40% 40%
No 80% 80% 60% 60%
Columntotals
100% 100% 100% 100%
Number ofrespondents
100 700 150 50
Desire to Travel Abroad by AgeDesire to Travel Abroad by AgeTable 15.10Table 15.10
Desire to Travel Abroad Age
Less than 45 45 or More
Yes 50% 50%
No 50% 50%
Column totals 100% 100%
Number of respondents 500 500
Desire to Travel AbroadDesire to Travel Abroadby Age and Sexby Age and Sex
Table 15.11Table 15.11
Desire toTravelAbroad
Sex Male Age
Female Age
< 45 >=45 <45 >=45
Yes 60% 40% 35% 65%
No 40% 60% 65% 35%
Columntotals
100% 100% 100% 100%
Number ofCases
300 300 200 200
Eating Frequently in Fast Food Eating Frequently in Fast Food Restaurants by Family SizeRestaurants by Family Size
Table 15.12Table 15.12
Eat Frequently in FastFood Restaurants
Family Size
Small Large
Yes 65% 65%
No 35% 35%
Column totals 100% 100%
Number of cases 500 500
Chi-Square DistributionChi-Square DistributionFigure 15.8Figure 15.8
Reject H0
Do Not Reject H0
CriticalValue
2
Independent Samples
One Sample Two or More Samples
One Sample Two or More Samples
Paired Samples Independent
SamplesPaired
Samples
* t test * Z test
* Chi-Square * K-S * Runs* Binomial
* Two-Group t test
* Z test
* Pairedt test * Chi-Square
* Mann-Whitney* Median* K-S
* Sign* Wilcoxon* McNemar* Chi-Square
Hypothesis Tests
Parametric Tests (Metric Tests)
Non-parametric Tests (Nonmetric Tests)
A Classification of Hypothesis Testing A Classification of Hypothesis Testing Procedures for Examining DifferencesProcedures for Examining Differences
Fig. 15.9Fig. 15.9
Eating Frequently in Fast Food Eating Frequently in Fast Food Restaurants by Family Size & IncomeRestaurants by Family Size & Income
Table 15.13Table 15.13
EatFrequentlyin Fast FoodRestaurants
Income Low Family size
High Family size
Small Large Small Large
Yes 65% 65% 65% 65%
No 35% 35% 35% 35%
Columntotals
100% 100% 100% 100%
Number ofRespondents
250 250 250 250
Two Independent-Samples Two Independent-Samples tt Tests TestsTable 15.14Table 15.14
Summary Statistics
Number Standardof Cases Mean Deviation
Male 15 9.333 1.137Female 15 3.867 0.435
F Test for Equality of Variances
F 2-tailvalue probability
15. 507 .000
t Test
Equal Variances Assumed Equal Variances Not Assumed
t Degrees of 2-tail t Degrees of 2-tailvalue freedom probability value freedom probability
4.492 28 . 000 -4.492 18.014 .000-
Number Standard StandardVariable of Cases Mean Deviation Error
Internet Attitude 30 5.167 1.234 .225Technology Attitude 30 4.100 1.398 .255
Difference = Internet - Technology
Difference Standard Standard 2-tail t Degrees of 2-tailMean deviation error Correlation prob. value freedom probability
1.067 0.828 .1511 .809 .000 7.059 29 .000
Paired-Samples Paired-Samples tt Test TestTable 15.15Table 15.15
K-S One-Sample Test forK-S One-Sample Test forNormality For Internet UsageNormality For Internet Usage
Table 15.16Table 15.16
Test Distribution - Normal
Mean: 6.600Standard Deviation: 4.296
Cases: 30
Most Extreme DifferencesAbsolute Positive Negative K-S z 2-Tailed p.222 .222 - .142 1.217 .103
Mann-Whitney U - Wilcoxon Rank Mann-Whitney U - Wilcoxon Rank Sum W Test Sum W Test
Internet Usage by SexInternet Usage by Sex
Table 15.17Table 15.17
Sex Mean Rank Cases
Male 20.93 15Female 10.07 15
Total 30
Corrected for tiesU W z 2-tailed p
31.000 151.000 -3.406 .001
NoteU = Mann-Whitney test statisticW = Wilcoxon W Statisticz = U transformed into a normally distributed z statistic.
Wilcoxon Matched-PairsWilcoxon Matched-PairsSigned-Rank TestSigned-Rank Test
Internet With TechnologyInternet With Technology
Table 15.18Table 15.18
(Technology - Internet) Cases Mean rank
-Ranks 23 12.72
+Ranks 1 7.50
Ties 6
Total 30
z = -4.207 2-tailed p = .0000
A Summary of Hypothesis Tests A Summary of Hypothesis Tests Related to DifferencesRelated to Differences
Table 15.19Table 15.19
Sample Application Level of Scaling Test/Comments
One Sample
One sample Distributions Nonmetric K-S and chi-square forgoodness of fitRuns test for randomnessBinomial test for goodness offit for dichotomous variables
One sample Means Metric t test, if variance is unknownz test, if variance is known
One Sample Proportions Metric z test
Contd.Contd.
Two Independent Samples
Two independent samples Distributions Nonmetric K-S two-sample test for examining theequivalence of two distributions
Two independent samples Means Metric Two-group t testF test for equality of variances
Two independent samples Proportions Metric z testNonmetric Chi-square test
Two independent samples Rankings/Medians Nonmetric Mann-Whitney U test is morepowerful than the median test
Paired Samples
Paired samples Means Metric Paired t test
Paired samples Proportions Nonmetric McNemar test for binary variablesChi-square test
Paired samples Rankings/Medians Nonmetric Wilcoxon matched-pairs ranked-signs test is more powerful than the sign test
Table 15.19 Contd.Table 15.19 Contd.
RIP15.1RIP15.1
In the 90s, the trend is toward global marketing. How can marketers In the 90s, the trend is toward global marketing. How can marketers market a brand abroad where there exists diverse historical and market a brand abroad where there exists diverse historical and cultural differences. According to Bob Kroll, the former president of cultural differences. According to Bob Kroll, the former president of Del Monte International, uniform packaging may be an asset, yet, Del Monte International, uniform packaging may be an asset, yet, catering to individual countries' culinary taste preferences is more catering to individual countries' culinary taste preferences is more important. One recent survey on international product marketing important. One recent survey on international product marketing makes this clear. Marketing executives now believe it's best to think makes this clear. Marketing executives now believe it's best to think globally but act locally. Respondents included 100 brand and globally but act locally. Respondents included 100 brand and product managers and marketing people from some of the nation's product managers and marketing people from some of the nation's largest food, pharmaceutical, and personal product companies. 39% largest food, pharmaceutical, and personal product companies. 39% said that it would not be a good idea to use uniform packaging in 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 foreign markets while 38% were in favor of it. Those in favor of regionally targeted packaging, however, mentioned the desirability of regionally targeted packaging, however, mentioned the desirability of maintaining as much brand equity and package consistency as maintaining as much brand equity and package consistency as possible from market to market.possible from market to market.
International Brand Equity - The International Brand Equity - The Name Of The GameName Of The Game
RIP15.1 Contd.RIP15.1 Contd.
But they also believed it was necessary to tailor the package to fit But they also believed it was necessary to tailor the package to fit the linguistic and regulatory needs of different markets. Based on the linguistic and regulatory needs of different markets. Based on this finding, a suitable research question can be: Do consumers in this finding, a suitable research question can be: Do consumers in different countries prefer to buy global name brands with different different countries prefer to buy global name brands with different packaging customized to suit their local needs? Based on this packaging customized to suit their local needs? Based on this research question, one can frame a hypothesis that other things being research question, one can frame a hypothesis that other things being constant, standardized branding with customized packaging for a constant, standardized branding with customized packaging for a well established name brand will result in greater market share. The well established name brand will result in greater market share. The hypotheses may be formulated as follows:hypotheses may be formulated as follows:
H0: Standardized branding with customized packaging for a well H0: Standardized branding with customized packaging for a well established name brand will not lead to greater market share in the established name brand will not lead to greater market share in the international market.international market.
H1: Other factors remaining equal, standardized branding with H1: Other factors remaining equal, standardized branding with customized packaging for a well established name brand will lead to customized packaging for a well established name brand will lead to greater market share in the international market.greater market share in the international market.
RIP15.1 Contd.RIP15.1 Contd.
To test the null hypothesis, a well established brand like Colgate To test the null hypothesis, a well established brand like Colgate toothpaste which has followed a mixed strategy can be selected. toothpaste which has followed a mixed strategy can be selected. The market share in countries with standardized branding and The market share in countries with standardized branding and standardized packaging can be compared with market share in standardized packaging can be compared with market share in countries with standardized branding and customized packaging, countries with standardized branding and customized packaging, after controlling for the effect of other factors. A two after controlling for the effect of other factors. A two independent samples t test can be usedindependent samples t test can be used..
RIP15.2RIP15.2
Descriptive statistics indicate that the public perception of Descriptive statistics indicate that the public perception of ethics in business, and thus ethics in marketing, are poor. ethics in business, and thus ethics in marketing, are poor. In a poll conducted by Business Week, 46% of those In a poll conducted by Business Week, 46% of those surveyed said that the ethical standards of business surveyed said that the ethical standards of business executives are only fair. A Time magazine survey revealed executives are only fair. A Time magazine survey revealed that 76% of Americans felt that business managers (and that 76% of Americans felt that business managers (and thus researchers) lacked ethics and this lack contributes to thus researchers) lacked ethics and this lack contributes to the decline of moral standards in the U.S. However, the the decline of moral standards in the U.S. However, the general public is not alone in its disparagement of business general public is not alone in its disparagement of business ethics. In a Touche Ross survey of businesspersons, results ethics. In a Touche Ross survey of businesspersons, results showed that the general feeling was that ethics were a showed that the general feeling was that ethics were a serious concern and media portrayal of the lack of ethics in serious concern and media portrayal of the lack of ethics in business has not been exaggerated.business has not been exaggerated.
Statistics Describe DistrustStatistics Describe Distrust