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Chapter XV Chapter XV Frequency Frequency Distribution, Distribution, Cross-Tabulation, Cross-Tabulation, and Hypothesis and Hypothesis Testing Testing Chapter XV

Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

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Page 1: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

Chapter XVChapter XV

Frequency Distribution, Frequency Distribution, Cross-Tabulation, and Cross-Tabulation, and

Hypothesis TestingHypothesis Testing

Chapter XV

Page 2: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis 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

Page 3: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

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

Page 4: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

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

Page 5: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

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

Page 6: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

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

Page 7: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

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

Page 8: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

Skewness of a DistributionSkewness of a DistributionFigure 15.2Figure 15.2

Skewed Distribution

Symmetric Distribution

Mean Median Mode

(a)

Mean Median Mode (b)

Page 9: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

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,

Page 10: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

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

Page 11: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

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

Page 12: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

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

Page 13: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

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

Page 14: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

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

Page 15: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

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%

Page 16: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

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

Page 17: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

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%

Page 18: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

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

Page 19: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

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

Page 20: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

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

Page 21: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

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

Page 22: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

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

Page 23: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

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

Page 24: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

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

Page 25: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

Chi-Square DistributionChi-Square DistributionFigure 15.8Figure 15.8

Reject H0

Do Not Reject H0

CriticalValue

2

Page 26: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

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

Page 27: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

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

Page 28: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

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-

Page 29: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

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

Page 30: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

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

Page 31: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

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.

Page 32: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

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

Page 33: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

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.

Page 34: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

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.

Page 35: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

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

Page 36: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

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.

Page 37: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

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..

Page 38: Chapter XV Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Chapter XV

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