probelm set 2 spring 2013

7/30/2019 Probelm Set 2 Spring 2013

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Biostatistics Spring 2013 Problem Set 2 Due Date: right before your final exam

1. Patients suffering from rheumatic diseases or osteoporosis often suffer critical losses in bone

mineral density (BMD). Alendronate is one medication prescribed to build or prevent further

loss of BMD. A study looked at 96 women taking alendronate to determine if a difference

existed in the mean percent change in BMD among five different primary diagnosis

classifications. Group 1 patients were diagnosed with rheumatoid arthritis (RA). Group 2

patients were a mixed collection of patients with diseases including lupus, Wegeners

granulomatosis and polyarteritis, and other vasculitic diseases (LUPUS). Group 3 patients had

polymyalgia rheumatic or temporal arthritis (PMRTA). Group 4 patients had osteoarthritis (OA)

and group 5 patients had osteoporosis (O) with no other rheumatic diseases identified in the

medical record. Changes in BMD are shown in the following table.

Diagnosis

RA LUPUS PMRTA OA O

11.091 2.961 -3.669 11.146 2.937

24.414 0.293 -7.816 -0.838 15.968

10.025 8.394 4.563 4.082 5.349-3.156 2.832 -0.093 6.645 1.719

6.835 -1.369 -0.185 4.329 6.45

3.321 11.288 1.302 1.234 20.243

1.493 30997 5.299 -2.817 3.290

-1.864 7.260 10.734 3.544 8.992

5.386 5.546 1.399 4.160 6.120

3.868 0.497 1.160 25.655

6.209 0.592 -0.247

-5.640 3.950 5.372

3.514 0.674 6.721

-2.308 9.354 9.950

15.981 2.610 10.820

-9.646 5.682 7.280

5.188 6.605

-1.892 7.507

16.553 5.075

7.412 0.163

5.559 12.767

4.761 3.481

-3.527 0.917

4.839 15.8531.850

-3.933

9.669

4.659

1.137

7.521

0.073


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-8.684

-0.372

21.311

10.831

3.351

9.557

Determine if you can conclude that there is a difference among population means. If there is a

difference, which group(s) above is (are) different? Let = 0.05 for your tests.

2. A study reported the effects of chewing one piece of nicotine gum (containing 2 mg nicotine)

on tic frequency in patients whose Tourettes disorder was inadequately controlled by

haloperidol. The following are the tic frequencies under four conditions:

Number of Tics during 30-Minute Period

After End of Chewingpatient baseline Gum chewing 0-30 minutes 30-60 minutes

1 249 108 93 59

2 1095 593 600 861

3 83 27 32 61

4 569 363 342 312

5 368 141 167 180

6 326 134 144 158

7 324 126 312 260

8 95 41 63 71

9 413 365 282 321

10 332 293 525 455

3. Researchers at a trauma center wished to develop a program to help brain-damaged trauma

victims regain an acceptable level of independence. An experiment involving 72 subjects with

the same degree of brain damage was conducted. The objective was to compare different

combinations of psychiatric treatment and physical therapy. Each subject was assigned to one of

24 different combinations of four types of psychiatric treatment and six physical therapy

programs. There were three subjects in each combination. The response variable is the number of

months elapsing between initiation of therapy and time at which the patient was able to function

independently. The results were as follows:


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Physical

therapy

program

Psychiatric Treatment

A B C D

I

11.0 9.4 12.5 13.2

9.6 9.6 11.5 13.2

10.8 9.6 10.5 13.5

II

10.5 10.8 10.5 15.0

11.5 10.5 11.8 14.6

12.0 10.5 11.5 14.0

III

12.0 11.5 11.8 12.8

11.5 11.5 11.8 13.7

11.8 12.3 12.3 13.1

IV

11.5 9.4 13.7 14.0

11.8 9.1 13.5 15.0

10.5 10.8 12.5 14.0

V

11.0 11.2 14.4 13.0

11.2 11.8 14.2 14.210.0 10.2 13.5 13.7

VI

11.2 10.8 11.5 11.8

10.8 11.5 10.2 12.8

11.8 10.2 11.5 12.0

Can one conclude one the basis of these data that the different psychiatric treatment programs

have different effects? Can one conclude that the physical therapy programs differ in

effectiveness? Can one conclude that there is interaction between psychiatric treatment programs

and physical therapy programs? Let

=0.05 for each test.

4. Research group studied diabetics insured by two employers. Group 1 subjects were employed

by the city of Asheville, North Carolina, and group 2 subjects were employed by Mission-St.

Josephs Health System. At the start of the study, the researchers performed the Mann-Whitney

U test to determine if a significant difference in weight existed between the two study groups.

The data are displayed in the following table.

Weight (lbs)

Group 1 Group 2

252 215 240 185 195 220

240 190 302 310 210 295205 270 312 212 190 202

200 159 126 238 172 268

170 204 268 184 190 220

170 215 215 136 140 311

320 254 183 200 280 164

148 164 287 270 264 206

214 288 210 200 270 170


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270 138 225 212 210 190

265 240 258 182 192

203 217 221 225 126

5. The following table shows the pesticide residue levels (ppb) in blood samples from fourpopulations of human subjects. Use the Kruskal-Wallis test to test at the 0.05 level of significant

the null hypothesis that there is no difference among the populations with respect to average

level of pesticide residue.

Population

A B C D

10 4 15 7

37 35 5 11

12 32 10 10

31 19 12 8

11 33 6 29 18 6 5

44 11 9 4

12 7 11 5

15 32 9 2

42 17 14 6

23 8 15 3

probelm set 2 spring 2013

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