Inference for Two-Way Tables

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Week 6 reflection and case study: Chapter 9 Inference for Two-Way Tables.

Reflection:

Discuss the use of two-way tables in general and relate to the results obtained for the HMO study

using proportions. The HMO study is repeated here for reference.

A study was designed to find reasons why patients leave a health maintenance organization (HMO). Patients were classified as to whether or not they had filed a complaint with the HMO. We want to compare the proportion of complainers who leave the HMO with the proportion of those who do not file complaints but who also leave the HMO. In the year of the study, 639 patients filed complaints, and 54 of these patients left the HMO voluntarily. For comparison, the HMO chose an SRS of 743 patients who had not filed complaints. Twenty-two of these patients left voluntarily. Previously we looked at this business problem using proportions. Discuss how to use the Chi- squared distribution and present specific results comparing to the results obtained using proportions.

Case study:

To design effective marketing strategy you need to know your customers. What are the

characteristics of people who use the World Wide Web to collect information on travel, and how do

they differ from those who do not and use other sources? A survey that collected data to address

this question examined the responses of 1401 Web users (WWW) and 1080 people who used other

sources for this information (no, other category).The following tables (Week06CaseStudy.xls) give

counts of WWW (WWW Yes) and Other (WWW no) for various demographic characteristics. Note

that the marginal sums are sometimes less than 1401 and 1080 because of missing data. Use the

methods of this chapter to compare the two groups (WWW Yes and Other, WWW No). Include

graphical and numerical summaries along with the results of your significance tests. In some cases

you may want to combine some categories for the demographic variables. Be sure to include a

discussion of missing values. Write a report summarizing your work.

Available data by demographic category in file Week06CaseStudy.xls covers:

 Age in years.

 Gender.

 Education.

 Occupational category.

 Household income (U.S. $).

 Race.

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Age WWWUserA CountA

Under18 Yes 22

18to25 Yes 160

26to35 Yes 328

36to45 Yes 277

46to55 Yes 224

Over55 Yes 101

Under18 No 24

18to25 No 161

26to35 No 184

36to45 No 189

46to55 No 164

Over55 No 109

Gender WWWUserB CountB

Female Yes 709

Male Yes 423

Female No 561

Male No 291

Education WWWUserC CountC

Grammar Yes 4

HighSchool Yes 85

Vocational Yes 54

SomeCollege Yes 336

College Yes 357

PostGrad Yes 259

Professional Yes 27

Other Yes 10

Grammar No 15

HighSchool No 125

Vocational No 53

SomeCollege No 293

College No 218

PostGrad No 114

Professional No 17

Other No 17

Occupation WWWUserD CountD

Mgmt Yes 167

Prof Yes 264

Educ Yes 175

Computer Yes 309

Other Yes 217

Mgmt No 87

Prof No 156

Educ No 164

Computer No 164

Other No 281

Income WWWUserE CountE

Lt10K Yes 43

10to20K Yes 58

20to30K Yes 116

30to40K Yes 149

40to50K Yes 127

50to75K Yes 259

75to100K Yes 119

Over100K Yes 134

NoAnswer Yes 127

Lt10K No 65

10to20K No 78

20to30K No 102

30to40K No 127

40to50K No 105

50to75K No 129

75to100K No 71

Over100K No 47

NoAnswer No 128

Race WWWUserF CountF

Cauc Yes 1001

Afr Yes 20

Asian Yes 35

Hisp Yes 20

Other Yes 56

Cauc No 772

Afr No 16

Asian No 16

Hisp No 15

Other No 33