chapter15.ppt 737KB Dec 31 1997 01:35:22 PM

(1)

Chapter XV

Frequency Distribution,

Cross-Tabulation, and

Hypothesis Testing

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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

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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

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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

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12) Internet and Computer Applications

13) Focus on Burke

14) Summary

15) Key Terms and Concepts

16) Acronyms

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RESPONDENT SEX FAMILIARITY INTERNET ATTITUDE TOWARD USAGE OF INTERNET

NUMBER USAGE Internet Technology

Shopping Banking

1 1.00 7.00 14.007.00 6.00 1.001.00 2 2.00 2.00 2.003.00 3.00 2.002.00 3 2.00 3.00 3.004.00 3.00 1.002.00

4 2.00 3.00 3.007.00 5.00 1.002.00 5 1.00 7.00 13.007.00 7.00 1.001.00

6 2.00 4.00 6.005.00 4.00 1.002.00 7 2.00 2.00 2.004.00 5.00 2.002.00 8 2.00 3.00 6.005.00 4.00 2.002.00 9 2.00 3.00 6.006.00 4.00 1.002.00 10 1.00 9.00 15.007.00 6.00 1.002.00 11 2.00 4.00 3.004.00 3.00 2.002.00 12 2.00 5.00 4.006.00 4.00 2.002.00 13 1.00 6.00 9.006.00 5.00 2.001.00 14 1.00 6.00 8.003.00 2.00 2.002.00 15 1.00 6.00 5.005.00 4.00 1.002.00 16 2.00 4.00 3.004.00 3.00 2.002.00 17 1.00 6.00 9.005.00 3.00 1.001.00 18 1.00 4.00 4.005.00 4.00 1.002.00 19 1.00 7.00 14.006.00 6.00 1.001.00 20 2.00 6.00 6.006.00 4.00 2.002.00 21 1.00 6.00 9.004.00 2.00 2.002.00 22 1.00 5.00 5.005.00 4.00 2.001.00 23 2.00 3.00 2.004.00 2.00 2.002.00 24 1.00 7.00 15.006.00 6.00 1.001.00

25 2.00 6.00 6.00 5.00 3.00 1.002.00 26 1.00 6.00 13.00 6.00 6.00 1.001.00 27 2.00 5.00 4.00 5.00 5.00 1.001.00 28 2.00 4.00 2.00 3.00 2.00 2.002.00 29 1.00 4.00 4.00 5.00 3.00 1.002.00 30 1.00 3.00 3.00 7.00 5.00 1.002.00

Internet Usage Data

Table 15.1

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Frequency Histogram

[image:7.720.3.700.71.497.2]

Frequency Histogram

Figure 15.1

Figure 15.1

2 3 4 ₅ ₆ ₇

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Skewness of a Distribution

[image:8.720.27.695.79.476.2]

Skewness of a Distribution

Figure 15.2

Figure 15.2

Skewed Distribution Symmetric Distribution

Mean Median

Mode (a)

(9)

Formulate H₀ and H₁

Steps Involved in Hypothesis Testing

[image:9.720.57.692.35.531.2]

Steps Involved in Hypothesis Testing

Fig. 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

(10)

Probabilities of Type I & Type II Error

Figure 15.4

Figure 15.4

99% of Total Area

Critical Value of Z

_= 15

_ = 17

 = 0.01

= 1.645 Z 

= -2.33 Z_

Z Z

95% of Total Area

(11)

Unshaped Area

= 0.0336

[image:11.720.55.670.85.434.2]

Probability of z with a One-Tailed Test

Fig. 15.5

Shaded Area

= 0.9664

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Hypothesis Tests

Distributions

A Broad Classification of Hypothesis Tests

Tests of Association

Tests of Differences

Median/ Rankings

[image:12.720.66.693.33.442.2]

Means Proportions

Figure 15.6

(13)

Frequency Distribution of Familiarity

with the Internet

[image:13.720.42.690.119.462.2]

with the Internet

Table 15.2

Table 15.2

Valid Cumulative Value label Value Frequency ( N) Percentage percentage percentage Not so familiar 1 0 0.0 0.0 0.0

2 2 6.7 6.9 6.9

3 6 20.0 20.7 27.6

4 6 20.0 20.7 48.3

5 3 10.0 10.3 58.6

6 8 26.7 27.6 86.2

Very familiar 7 4 13.3 13.8 100.0

Missing 9 1 3.3

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[image:14.720.43.697.106.497.2]

Gender and Internet Usage

Table 15.3

Table 15.3

Sex

Row

Internet Usage Male Female Total

Light (1) 5 10 15

Heavy (2) 10 5 15

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[image:15.720.25.687.110.476.2]

Internet Usage by Sex

Table 15.4

Table 15.4

Sex

Internet Usage

Male

Female

Light

33.3%

66.7%

Heavy

66.7%

33.3%

(16)

Original Two Variables

Introduce a Third Variable

Some Association between the Two

Variables

Introduction of a Third Variable in

[image:16.720.60.684.35.507.2]

Cross-Tabulation

Fig. 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

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[image:17.720.63.681.139.526.2]

Sex by Internet Usage

Table 15.5

Table 15.5

Internet Usage

Sex

Light

Heavy

Total

Male

33.3%

66.7%

100.0%

(18)

Purchase of Fashion Clothing by

[image:18.720.36.703.75.511.2]

Marital Status

Table 15.6

Table 15.6

Purchase of

Fashion Current Marital Status

Clothing Married Unmarried

High 31% 52%

Low 69% 48%

Column 100% 100%

Number of

(19)

Purchase of Fashion Clothing by

[image:19.720.45.687.28.501.2]

Marital Status

Table 15.7

Table 15.7

Purchase of

Fashion SexMale Female

Clothing Married Not

Married Married MarriedNot

High 35% 40% 25% 60%

Low 65% 60% 75% 40%

Column

totals 100% 100% 100% 100%

Number of

cases 400 120 300 180

(20)

Ownership of Expensive

[image:20.720.37.692.58.505.2]

Automobiles by Education Level

Table 15.8

Table 15.8

Own Expensive

Automobile Education

College Degree No College Degree

Yes 32% 21%

No 68% 79%

Column totals 100% 100%

(21)

Ownership of Expensive Automobiles

by Education Level and Income Levels

Table 15.9

Table 15.9

Own

Expensive IncomeLow Income High Income

Automobile College

Degree CollegeNo Degree

College

Degree CollegeNo Degree

Yes 20% 20% 40% 40%

No 80% 80% 60% 60%

Column

totals 100% 100% 100% 100%

Number of

(22)

[image:22.720.25.689.26.526.2]

Desire to Travel Abroad by Age

Table 15.10

Table 15.10

Desire to Travel Abroad Age

Less than 45 45 or More

Yes 50% 50%

No 50% 50%

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Desire to Travel Abroad

[image:23.720.44.685.44.499.2]

by Age and Sex

Table 15.11

Table 15.11

Desire to Travel Abroad

Sex Male

Age Female Age

< 45 >=45 <45 >=45

Yes 60% 40% 35% 65%

No 40% 60% 65% 35%

Column

totals 100% 100% 100% 100%

Number of

(24)

Eating Frequently in Fast Food

[image:24.720.80.686.23.518.2]

Restaurants by Family Size

Table 15.12

Table 15.12

Eat Frequently in Fast

Food Restaurants Family Size

Small Large

Yes 65% 65%

No 35% 35%

(25)

[image:25.720.54.640.109.426.2]

Chi-Square Distribution

Figure 15.8

Figure 15.8

Reject H₀ Do Not Reject

H₀

Critical Value

(26)

Independent Samples

One Sample Two or More Samples

One Sample Two or More Samples Paired Samples Independent Samples Paired Samples

* t test

* Z test * Chi-Square * K-S * Runs

* Binomial

* Two-Group t test

* Z test

* Paired

t test * Chi-Square_{* Mann-Whitney} * Median

* K-S

* Sign

* Wilcoxon * McNemar

* Chi-Square

Hypothesis Tests

Parametric Tests (Metric Tests)

Non-parametric Tests (Nonmetric Tests)

[image:26.720.21.683.50.521.2]

A Classification of Hypothesis Testing

Procedures for Examining Differences

Fig. 15.9

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Eating Frequently in Fast Food

Restaurants by Family Size & Income

[image:27.720.38.683.37.485.2]

Restaurants by Family Size & Income

Table 15.13

Table 15.13

Eat

Frequently in Fast Food Restaurants

Income Low

Family size High Family size

Small Large Small Large

Yes 65% 65% 65% 65%

No 35% 35% 35% 35%

Column

totals 100% 100% 100% 100%

Number of

(28)

Two Independent-Samples

[image:28.720.47.714.69.502.2]

Two Independent-Samples

t

Tests

Table 15.14

Table 15.14

Summary Statistics

Number Standard

of Cases Mean Deviation

Male 15 9.333 1.137

Female 15 3.867 0.435

F Test for Equality of Variances

F 2tail

value probability

15. 507 .000

t Test

Equal Variances Assumed Equal Variances Not Assumed

t Degrees of 2tail t Degrees of 2tail

value freedom probability value freedom probability

4.492 28 . 000 4.492 18.014 .000

(29)

-Number Standard Standard

Variable of Cases Mean Deviation Error

Internet Attitude 30 5.167 1.234 .225

Technology Attitude 30 4.100 1.398 .255

Difference = Internet Technology

Difference Standard Standard 2tail t Degrees of 2tail Mean deviation error Correlation prob. value freedom probability

1.067 0.828 .1511 .809 .000 7.059 29 .000

Paired-Samples

[image:29.720.13.709.100.529.2]

Paired-Samples

t

Test

Table 15.15

(30)

K-S One-Sample Test for

Normality For Internet Usage

Table 15.16

Table 15.16

Test Distribution Normal

Mean: 6.600

Standard Deviation: 4.296

Cases: 30

Most Extreme Differences

Absolute Positive Negative KS z 2Tailed p

(31)

Mann-Whitney U - Wilcoxon Rank

Sum W Test

[image:31.720.1.720.40.515.2]

Internet Usage by Sex

Table 15.17

Table 15.17

Sex Mean Rank Cases

Male 20.93 15

Female 10.07 15

Total 30

Corrected for ties

U W z 2tailed p

31.000 151.000 3.406 .001

Note

U = MannWhitney test statistic

W = Wilcoxon W Statistic

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Wilcoxon Matched-Pairs

Signed-Rank Test

[image:32.720.26.712.88.470.2]

Internet With Technology

Table 15.18

Table 15.18

(Technology Internet) Cases Mean rank

Ranks 23 12.72

+Ranks 1 7.50

Ties 6

Total 30

(33)

A Summary of Hypothesis Tests

Related to Differences

Table 15.19

Table 15.19

Sample Application Level of Scaling Test/Comments

One Sample

One sample Distributions Nonmetric KS and chisquare 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

Contd.

(34)

Two Independent Samples

Two independent samples Distributions Nonmetric KS twosample test for examining the equivalence of two distributions

Two independent samples Means Metric Twogroup t test

F test for equality of variances

Two independent samples Proportions Metric z test

Nonmetric Chisquare test

Two independent samples Rankings/Medians Nonmetric MannWhitney U test is more powerful than the median test

Paired Samples

Paired samples Means Metric Paired t test

Paired samples Proportions Nonmetric McNemar test for binary variables Chisquare test

Paired samples Rankings/Medians Nonmetric Wilcoxon matchedpairs rankedsigns

test is more powerful than the sign test

Table 15.19 Contd.

Table 15.19 Contd.

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RIP15.1

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.

International Brand Equity - The

Name Of The Game

(36)

RIP15.1 Contd.

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.

(37)

RIP15.1 Contd.

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

(38)

RIP15.2

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.