A common symptom of otitis media in young children is the prolonged presence of
ID: 3435722 • Letter: A
Question
A common symptom of otitis media in young children is the prolonged presence of fluid in the middle ear, known as middle-ear effusion. The presence of fluid may result in temporary hearing loss and interfere with normal learning skills in the first 2 years of life. One hypothesis is that babies who are breastfed for at least 1 month build up some immunity against the effects of the infection and have less prolonged effusion than do bottle-fed babies. A small study of 24 pairs of babies is set up, in which the babies are matched on a one-to-one basis according to age, sex, socioeconomic status, and type of medications taken. One member of the matched pair is a breastfed baby, and the other member is a bottle-fed baby. The outcome variable is the duration of middle-ear effusion after the first episode of otitis media. Using the Wilcoxon signed-rank test, test the hypothesis that the duration of effusion is the same among breastfed babies and bottle-fed babies.
Breastfed
Bottle-fed
Breastfed
Bottle-fed
Breastfed
Bottle-fed
Breastfed
Bottle-fed
20
18
58
223
52
39
65
77
11
35
7
7
14
15
10
12
3
7
39
57
12
21
7
8
24
182
17
76
30
28
19
16
7
6
17
186
7
8
34
28
28
33
12
29
15
27
25
20
Breastfed
Bottle-fed
Breastfed
Bottle-fed
Breastfed
Bottle-fed
Breastfed
Bottle-fed
20
18
58
223
52
39
65
77
11
35
7
7
14
15
10
12
3
7
39
57
12
21
7
8
24
182
17
76
30
28
19
16
7
6
17
186
7
8
34
28
28
33
12
29
15
27
25
20
Explanation / Answer
Null Hypothesis, H0: Any difference between breastfed and bottlefed is due to chance.
Alternative Hypothesis, H1: Any difference between breastfed and bottlefed is not due to chance.
The value of the test statistics is the minimum of the sum of positive ranks and negative ranks.
Hence here, t=61.
From Wilcoxon Signed-Ranks Table, for n = 23 and alpha = 0.05, t critical = 73.
Since, t < t critical, we fail to reject H0 and conclude that any difference between breastfed and bottlefed is due to chance.
Breastfed Bottlefed Diff Abs Diff Rank of Abs Diff Positive Ranks Negative Ranks 20 18 2 2 6 6 11 35 -24 24 19 19 3 7 -4 4 9 9 24 182 -158 158 21 21 7 6 1 1 2.5 2.5 28 33 -5 5 10.5 10.5 58 223 -165 165 22 22 7 7 0 39 57 -18 18 18 18 17 76 -59 59 20 20 17 186 -169 169 23 23 12 29 -17 17 17 17 52 39 13 13 16 16 14 15 -1 1 2.5 2.5 12 21 -9 9 13 13 30 28 2 2 6 6 7 8 -1 1 2.5 2.5 15 27 -12 12 14.5 14.5 65 77 -12 12 14.5 14.5 10 12 -2 2 6 6 7 8 -1 1 2.5 2.5 19 16 3 3 8 8 34 28 6 6 12 12 25 20 5 5 10.5 10.5 61 215Related Questions
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