MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Serum estradiol is an important risk factor for breast cancer in postmenopausal women. To better understand the etiology of breast cancer, serum-estradiol samples were collected from 25 premenopausal women (at about the same time period of the menstrual cycle) of whom 10 were Caucasian and 15 were African American. Data were collected on both serum estradiol as well as body mass index (BMI) = weight (kg)/height2 (m2), which is an important measure of overall obesity. The data are shown in Table 9.16.
The distribution of serum estradiol is usually highly skewed (especially for premenopausal women), and we are reluctant to assume normality.
HW Question: What test can we use to compare the distribution of serum estradiol for Caucasian vs. African American women? Implement the test and report a two-tailed p-value based on large sample methods
Here's my approach and I'm not sure if this is correct.
I am using the Wilcoxon rank sum test for this problem.
Group 1 (African-American): n=15
Group 2 (Caucasian): n=10
Two tie groups (
R1=20+5+18+3+4+1+12*3+6+16+15+19+17+24=184
E(R1) = 15*(15+10+1)/2 = 195
g=2, t1 = 2, t2 = 3
Using the test statistic formula for R1 != E(R1) and ties, T= 0.583
p-value = 0.5599>0.05.
Failed to reject H_0. We conclude that the distribution of serum estradiol is not significantly different between Caucasian and African American women groups.
Transcribed Image Text:TABLE 9.15 (Weight change, control period) -
(weight change, lack-of-consistency
period) among 23 adolescent
diabetic boys
i
1
2
3
4
56780
A₁
-12.6
-10.3
-5.9
-5.4
-4.5
-2.7
-1.8
+0.3
i
9
10
11
12
13
14
15
16
+2.2
+3.5
+4.8
+5.4
+5.8
+6.0
+6.7
+9.6
17
18
19
20
21
22
23
Mean
sd
n
Δ.
+11.5
+12.2
+13.9
+14.2
+18.0
+18.6
+21.7
4.83
9.33
Data set available
23
9.47 Answer the question in Problem 9.45 if we are not
willing to make the assumption of normality.
9.48 Implement the test in Problem 9.47, and report a two-
tailed p-value.
Cancer
Serum estradiol is an important risk factor for breast
cancer in postmenopausal women. To better understand
the etiology of breast cancer, serum-estradiol samples
were collected from 25 premenopausal women (at about
the same time period of the menstrual cycle) of whom
10 were Caucasian and 15 were African American. Data
were collected on both serum estradiol as well as body
mass index (BMI) = weight (kg)/height² (m²), which is an
important measure of overall obesity. The data are shown
in Table 9.16.
The distribution of serum estradiol is usually highly skewed
(especially for premenopausal women), and we are reluc-
tant to assume normality.
9.49 What test can we use to compare the distribution
of serum estradiol for Caucasian vs. African American
women?
9.50 Implement the test in Problem 9.49, and report a two-
tailed p-value based on large sample methods.
9.51 Answer the question in Problem 9.50 using permuta-
tion test methods.
ID
TABLE 9.16 Relationship of serum estradiol, BMI,
and ethnicity in 25 premenopausal
women
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Serum estradiol
(pg/mL)
94
54
31
21
46
56
18
19
12
14
25
35
22
71
43
35
42
50
44
41
28
65
31
35
91
Estradiol rank
25
20
9.5
5
18
21
3
4
1
2
7
12
6
23
16
12
15
19
17
14
8
22
9.5
12
24
Problems
*1 = African-American, 0 = Caucasian.
BMI
18.9
19.7
20.7
23.4
23.3
25.1
35.6
26.2
22.3
20.4
21.7
20.0
21.0
21.8
32.7
23.6
24.7
23.2
33.9
20.6
24.7
26.3
20.1
22.5
29.1
Ethnic group*
1
1
1
0
0
1
1
0
369
1
1
1
1
1
9.53 Suppose we want to compare mean BMI between
Caucasian and Africa American premenopausal women
based on the data in the table and are willing to assume the
distribution of BMI is approximately normal. What test can
we use to make this comparison?
(Note that for Caucasian women, mean BMI = = 22.0,
sd = 2.47, n = 10; for African American women, mean
BMI = 25.4, sd = 5.01, n = = 15.)
9.54 Implement the test in Problem 9.53, and report a two-
tailed p-value.
Ophthalmology
9.52 Compare your results in Problems 9.50 and 9.51.
Another important variable in the epidemiology of breast
cancer is BMI, which has been found to be related to both all Refer to Data Set TEAR.DAT at www.cengagebrain.com. We
serum estradiol and ethnicity in previous studies.
want to compare tear break-up time (TBUT) immediately after
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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
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