Statistics - SPSS Projects

. This data was provided by Drs. Pan and Chi in the Department of Imaging Physics of UT MD Anderson Cancer

Problem 1 . This data was provided by Drs. Pan and Chi in the Department of Imaging Physics of UT MD Anderson Cancer Center. Please contact them if you wish to use the data. The data consists of measurements of the tumor sizes of over 200 different patient tumors. The tumor sizes were computed by two different methods and each line of data has the different measurements from a single tumor. For this study it was important that the methods did not differ at the = .01 level. As always, I want to see:

What is the question that you are trying to answer?
What are the null and alternative hypotheses?
What method will you use to test the hypotheses and what assumptions do you make in using this method?
What is the test statistic?
What is the rejection region?
What is the calculation procedure? Since I expect you to use a computer, give me enough information that I could reproduce your procedure.
State a conclusion?

Tumor volumes
PET-AVG	PET-HCT
111.41	109.99
2.05	0.64
3.42	3.52
4.55	4.25
3.67	4.69
9.05	4.89
5.67	5.04
7.38	6.90
6.80	6.95
9.58	9.39
15.79	15.31
16.15	16.54
22.84	24.45
49.93	41.76
68.75	67.28
252.85	246.25
1.47	0.44
0.88	0.49
1.13	0.78
1.47	1.27
3.13	2.30
7.48	4.50
5.04	4.60
1.08	0.29
0.68	0.68
1.52	1.42
1.52	1.52
3.42	2.89
8.17	3.13
2.74	3.28
5.48	4.01
5.57	5.97
6.21	6.41
14.28	8.46
11.83	11.88
15.35	12.08
29.58	27.97
33.15	29.00
45.77	43.52
62.51	60.50
87.83	84.21
101.81	96.62
349.66	346.77
0.59	0.29
0.93	0.54
0.59	0.59
1.81	0.69
0.69	0.74
1.03	0.98
1.13	1.13
2.01	1.42
1.71	1.47
2.01	1.61
2.59	1.66
2.79	1.96
2.10	2.00
2.45	2.74
2.64	2.79
3.47	2.98
4.21	3.28
3.91	3.72
4.85	4.50
4.30	5.00
6.21	5.77
5.82	5.77
7.14	6.02
9.54	7.78
9.44	10.81
17.07	14.08
21.12	17.95
21.03	20.83
31.15	26.41
45.08	45.67
70.38	67.25
136.67	131.83
0.59	0.44
0.93	0.54
0.68	0.59
0.78	0.83
1.61	1.61
4.65	3.38
3.47	3.42
4.69	5.43
5.82	6.06
7.39	7.93
6.21	9.44
32.91	29.09
29.00	30.37
1.81	0.39
1.96	0.64
0.78	1.03
1.32	1.22
1.52	1.47
1.81	1.76
2.64	1.96
2.01	2.45
2.40	2.69
4.50	4.60
4.06	4.74
9.16	7.00
8.56	8.46
14.47	13.98
24.36	24.51
39.75	37.21
81.20	75.29
0.29	0.49
0.78	0.73
5.09	4.89
7.48	7.04
87.19	92.91
0.29	0.24
0.98	0.93
1.22	1.08
1.81	1.86
2.11	1.86
4.16	2.10
2.49	2.64
2.79	2.69
3.03	3.23
4.89	3.42
3.86	3.57
5.92	7.09
7.68	8.61
11.54	8.85
20.15	11.54
13.31	11.84
20.83	19.81
31.98	30.81
209.78	187.63
279.08	269.69
470.52	448.71
0.68	0.64
0.73	0.69
0.54	0.69
0.78	0.83
1.03	0.88
5.77	1.56
2.93	1.61
3.48	2.55
3.91	2.79
5.23	3.13
4.74	3.62
4.40	3.77
7.77	6.36
9.93	8.07
10.32	10.81
11.54	14.33
25.97	23.72
30.12	27.29
124.87	120.13
179.27	159.66
2.05	0.10
0.64	0.83
9.73	1.86
3.42	2.25
11.54	8.85
11.49	10.42
11.78	10.90
10.02	12.47
10.22	12.91
15.99	13.94
17.76	15.75
25.97	26.94
33.25	30.46
165.86	172.07
3.18	1.42
4.69	4.40
9.98	8.61
11.30	10.66
23.24	16.79
49.47	47.61
67.78	61.13
123.93	116.06
1.03	0.93
1.32	1.37
3.96	1.86
3.23	2.54
7.78	4.70
13.10	10.56
50.67	23.97
45.70	40.10
109.34	107.53
1.66	0.20
1.27	0.29
2.89	0.73
1.76	2.49
37.95	33.40
148.76	129.25
0.44	0.24
1.22	0.39
2.45	0.59
6.11	4.74
11.69	11.59
22.59	20.49
27.87	27.09
85.77	85.62
169.78	160.73
3.62	2.79
83.77	88.08
6.65	5.62
95.55	85.38
1.03	1.27
74.41	75.29
1.32	0.78
0.73	0.15
20.34	17.07
181.10	183.80

Problem 2 . A common problem in medical physics is to measure the radiation dose to a specific point. For many purposes the preferred method is to expose film to a series of standardized radiation dosages which are determined using a different detector. The optical density of the film provides a curve that can be fitted to the standard dosages and in practice the optical density is measured and a radiation dosage calculated from the fitted curve. Data for this procedure is provided in a spread sheet provided by Dr. David Followill and Scott Davidson. You are to do a regression of optical density versus dose using multivariate regression model of the form:

\[OD(D)={{\beta }_{0}}+{{\beta }_{1}}D+{{\beta }_{2}}{{D}^{2}}+{{\beta }_{3}}{{D}^{3}}\]

where OD is the optical density at a dose level D. The parameters ₀ , … ₃ are the regression coefficients of the dose raised to the 0, 1,2 and 3 ^rd power. The question is what power do you need to fit the data to a curve. More generally, how much better is a third order than a second order fit? Prepare a table showing a goodness of fit values for the different degrees of polynomials.

Hint: This is actually a linear regression problem in the values of _i . with the D ⁱ each being a predictor variable. I realize that you will need to do some exploring to discover how to do these calculations, but it is a common type of problem.

Lot no. EBT 47171-01I

Run 1			Run 2			Run 3
film no	OD	film no	OD	film no	OD	Dose (cGy)
37	0.14	38	0.141	39	0.141	0
1	0.268	13	0.262	25	0.26	31
2	0.351	14	0.348	26	0.346	61
3	0.434	15	0.434	27	0.431	103
4	0.545	16	0.546	28	0.543	180
5	0.651	17	0.653	29	0.65	293
6	0.729	18	0.73	30	0.727	411
7	0.77	19	0.769	31	0.769	513
8	0.822	20	0.82	32	0.817	616
9	0.861	21	0.862	33	0.853	719
10	0.895	22	0.892	34	0.885	822
11	0.919	23	0.913	35	0.91	924

Problem 3 : A study was conducted to investigate drinking problems among college students. In 1983 a group of students were asked whether they had ever driven an automobile while drinking.

(At this time the legal drinking age was 18.) Four years later a similar study, after the drinking age was raised, was undertaken and the results for both studies are presented below:

Drove while drinking	Year	Year	Totals
	1983	1987
Yes	1250	991	2241
No	1387	1666	3053
Total	2637	2657	5294

Use the chi-square test to evaluate the null hypothesis that the proportions of students driving while drinking are the same in two calendar years.
Test the hypothesis that the proportions of students driving while drinking was the same in the two years.
Construct a 95% confidence interval for the true difference in population proportions.

Problem 4 . In Problem 4 researchers have measured radiation dosages,(mGy), to a range of sites in phantom (on an imitation 5 year old doll). There were 5 different protocols for irradiation using a CT scan and each different scan was measured at a series of different organs: Brain, left eye, right eye, head thyroid (dose received by the thyroid when scanning the head), chest thyroid (dose to thyroid when scanning the chest), sternum, left and right breasts and left and right lungs.

Assume that we do not have to consider interactions between different sites and protocols so that we can avoid doing a two-way analysis. But we do want to answer the following questions:

Using the different groups, is there a difference between groups assuming protocols are the same?
Assuming results at different sites can be treated the same, is there a difference in results for different protocols?

			dose
#	protocol	organ	mGy
1	axial	brain	63.65746
2	axial	brain	32.25414
3	axial	brain	32.33149
4	axial	brain	32.65055
5	axial	brain	32.51519
6	axial	brain	23.25
7	hel 0.516	brain	30.15708
8	hel 0.516	brain	31.12024
9	hel 0.516	brain	31.07354
10	hel 0.516	brain	30.7588
11	hel 0.516	brain	30.47006
12	hel 0.516	brain	28.71
13	hel 0.984	brain	31.65382
14	hel 0.984	brain	31.95048
15	hel 0.984	brain	31.22714
16	hel 0.984	brain	32.12614
17	hel 0.984	brain	31.10852
18	hel 0.984	brain	27.92
19	axial	left eye	68.05663
20	axial	left eye	33.74309
21	axial	left eye	34.70028
22	axial	left eye	34.64227
23	axial	left eye	34.30387
24	axial	left eye	18.14
25	hel 0.516	left eye	33.08838
26	hel 0.516	left eye	33.00144
27	hel 0.516	left eye	32.99111
28	hel 0.516	left eye	28.1293
29	hel 0.516	left eye	33.98833
30	hel 0.516	left eye	25.06
31	hel 0.984	left eye	32.97956
32	hel 0.984	left eye	28.8699
33	hel 0.984	left eye	33.03506
34	hel 0.984	left eye	28.36924
35	hel 0.984	left eye	27.64502
36	hel 0.984	left eye	21.55
37	axial	right eye	69.33287
38	axial	right eye	35.13536
39	axial	right eye	34.79696
40	axial	right eye	35.09669
41	axial	right eye	35.14503
42	axial	right eye	19.06
43	hel 0.516	right eye	30.3153
44	hel 0.516	right eye	33.93292
45	hel 0.516	right eye	30.30073
46	hel 0.516	right eye	32.72636
47	hel 0.516	right eye	35.15538
48	hel 0.516	right eye	23.71
49	hel 0.984	right eye	34.17699
50	hel 0.984	right eye	32.25488
51	hel 0.984	right eye	34.26212
52	hel 0.984	right eye	32.42364
53	hel 0.984	right eye	32.7796
54	hel 0.984	right eye	26.18
55	axial	head thyroid	88.76657
56	axial	head thyroid	49.13536
57	axial	head thyroid	47.78177
58	axial	head thyroid	43.00552
59	axial	head thyroid	44.05939
60	axial	head thyroid	39.51
61	hel 0.516	head thyroid	42.08172
62	hel 0.516	head thyroid	40.69813
63	hel 0.516	head thyroid	42.19909
64	hel 0.516	head thyroid	40.37805
65	hel 0.516	head thyroid	41.71964
66	hel 0.516	head thyroid	41.87
67	hel 0.984	head thyroid	41.60521
68	hel 0.984	head thyroid	40.3832
69	hel 0.984	head thyroid	41.20996
70	hel 0.984	head thyroid	41.34238
71	hel 0.984	head thyroid	41.61828
72	hel 0.984	head thyroid	37.96
73	axial	chest thyroid	49.78903
74	axial	chest thyroid	50.31312
75	axial	chest thyroid	50.83722
76	axial	chest thyroid	49.89385
77	axial	chest thyroid	50.31312
78	axial	chest thyroid	27.95
79	hel 0.516	chest thyroid	38.70304
80	hel 0.516	chest thyroid	38.39365
81	hel 0.516	chest thyroid	38.66436
82	hel 0.516	chest thyroid	38.09392
83	hel 0.516	chest thyroid	40.42403
84	hel 0.516	chest thyroid	26.7
85	hel 0.984	chest thyroid	40.70442
86	hel 0.984	chest thyroid	40.67541
87	hel 0.984	chest thyroid	39.96961
88	hel 0.984	chest thyroid	39.66022
89	hel 0.984	chest thyroid	39.93094
90	hel 0.984	chest thyroid	28.80
91	hel 1.375	chest thyroid	41.87431
92	hel 1.375	chest thyroid	41.90331
93	hel 1.375	chest thyroid	42.29972
94	hel 1.375	chest thyroid	41.75829
95	hel 1.375	chest thyroid	42.03867
96	hel 1.375	chest thyroid	27.36
97	axial	sternum	50.78486
98	axial	sternum	51.2037
99	axial	sternum	51.51784
100	axial	sternum	52.1461
101	axial	sternum	51.83197
102	axial	sternum	22.29
103	hel 0.516	sternum	39.3605
104	hel 0.516	sternum	39.93094
105	hel 0.516	sternum	40.23066
106	hel 0.516	sternum	39.28315
107	hel 0.516	sternum	39.80525
108	hel 0.516	sternum	27.55
109	hel 0.984	sternum	39.19613
110	hel 0.984	sternum	40.66575
111	hel 0.984	sternum	40.11464
112	hel 0.984	sternum	39.42818
113	hel 0.984	sternum	38.00691
114	hel 0.984	sternum	29.75
115	hel 1.375	sternum	49.46409
116	hel 1.375	sternum	32.0221
117	hel 1.375	sternum	48.51657
118	hel 1.375	sternum	48.87431
119	hel 1.375	sternum	46.70856
120	hel 1.375	sternum	33.58
121	axial	left breast	49.05529
122	axial	left breast	49.89385
123	axial	left breast	49.89385
124	axial	left breast	49.68421
125	axial	left breast	48.95047
126	axial	left breast	19.43
127	hel 0.516	left breast	37.38812
128	hel 0.516	left breast	38.82873
129	hel 0.516	left breast	38.75138
130	hel 0.516	left breast	39.08978
131	hel 0.516	left breast	36.25691
132	hel 0.516	left breast	25.39
133	hel 0.984	left breast	38.52901
134	hel 0.984	left breast	40.07597
135	hel 0.984	left breast	40.04696
136	hel 0.984	left breast	40.20166
137	hel 0.984	left breast	39.86326
138	hel 0.984	left breast	28.54
139	hel 1.375	left breast	32.06077
140	hel 1.375	left breast	46.97928
141	hel 1.375	left breast	46.73757
142	hel 1.375	left breast	46.96961
143	hel 1.375	left breast	45.97376
144	hel 1.375	left breast	19.9
145	axial	right breast	50.41794
146	axial	right breast	51.04685
147	axial	right breast	50.7324
148	axial	right breast	49.68421
149	axial	right breast	49.68421
150	axial	right breast	25.99
151	hel 0.516	right breast	38.80939
152	hel 0.516	right breast	37.23343
153	hel 0.516	right breast	37.75552
154	hel 0.516	right breast	36.43094
155	hel 0.516	right breast	38.47099
156	hel 0.516	right breast	31.48
157	hel 0.984	right breast	37.39779
158	hel 0.984	right breast	38.94475
159	hel 0.984	right breast	38.06492
160	hel 0.984	right breast	39.3895
161	hel 0.984	right breast	36.78867
162	hel 0.984	right breast	30.11
163	hel 1.375	right breast	46.95994
164	hel 1.375	right breast	31.57735
165	hel 1.375	right breast	45.03591
166	hel 1.375	right breast	45.69337
167	hel 1.375	right breast	45.41298
168	hel 1.375	right breast	36.42
169	axial	left lung	38.46857
170	axial	left lung	36.26737
171	axial	left lung	35.74328
172	axial	left lung	38.0493
173	axial	left lung	38.15412
174	axial	left lung	27.58
175	hel 0.516	left lung	31.15193
176	hel 0.516	left lung	30.05939
177	hel 0.516	left lung	29.80801
178	hel 0.516	left lung	30.7942
179	hel 0.516	left lung
180	hel 0.516	left lung	31.81
181	hel 0.984	left lung	31.98343
182	hel 0.984	left lung	33.54006
183	hel 0.984	left lung	33.68508
184	hel 0.984	left lung	33.64641
185	hel 0.984	left lung	30.38812
186	hel 0.984	left lung	31.97
187	hel 1.375	left lung	36.18923
188	hel 1.375	left lung	35.77348
189	hel 1.375	left lung	33.54972
190	hel 1.375	left lung	32.89227
191	hel 1.375	left lung	33.42403
192	hel 1.375	left lung	34.57
193	axial	right lung	39.97285
194	axial	right lung	40.70726
195	axial	right lung	41.12692
196	axial	right lung	41.12692
197	axial	right lung	40.39251
198	axial	right lung	26.01
199	hel 0.516	right lung	31.46133
200	hel 0.516	right lung	30.72652
201	hel 0.516	right lung	31.14227
202	hel 0.516	right lung	31.09392
203	hel 0.516	right lung	32.31215
204	hel 0.516	right lung	30.32
205	hel 0.984	right lung	31.62569
206	hel 0.984	right lung	30.37845
207	hel 0.984	right lung	30.85221
208	hel 0.984	right lung	30.18508
209	hel 0.984	right lung	31.58702
210	hel 0.984	right lung	27.05
211	hel 1.375	right lung	34.99033
212	hel 1.375	right lung	31.75138
213	hel 1.375	right lung	36.0732
214	hel 1.375	right lung	34.91298
215	hel 1.375	right lung	34.73895
216	hel 1.375	right lung	36.89

Problem 5 . A study in Italy compared the treatment of women with breast cancer by different specialties. There possible treatments for radical surgery regardless of age (R), conservative surgery only for younger patients (CR) and conservative surgery regardless of age (C). The results were:

Specialty	R	CR	C	Total
Internal	6	22	42	70
Surgery	23	61	127	211
Radiotherapy	2	3	54	59
Oncology	1	12	43	56
Gynecology	1	12	31	44
Total	33	110	297	440

At the .05 level of significance, test the null hypothesis that there is no association between physician specialty and recommended treatment
What do you conclude?

Price: $34.93

Solution: The downloadable solution consists of 21 pages, 1393 words and 19 charts.
Deliverable: Word Document