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694 CHAPTER 13 NONPARAMETRIC AND DISTRIBUTION-FREE STATISTICS
13.3.2 Determining the effects of grapefruit juice on pharmacokinetics of oral digoxin (a drug often prescribed
for heart ailments) was the goal of a study by Parker et al. (A-1). Seven healthy nonsmoking
volunteers participated in the study. Subjects took digoxin with water for 2 weeks, no digoxin
for 2 weeks, and digoxin with grapefruit juice for 2 weeks. The average peak plasma digoxin
concentration (Cmax) when subjects took digoxin with water is given in the first column of the
following table. The second column gives the Cmax concentration when subjects took digoxin with
grapefruit juice. May we conclude on the basis of these data that the Cmax concentration is higher
when digoxin is taken with grapefruit juice Let a = .05.
Cmax
Subject
H 2 O
GFJ
1 2.34 3.03
2 2.46 3.46
3 1.87 1.97
4 3.09 3.81
5 5.59 3.07
6 4.05 2.62
7 6.21 3.44
Source: Robert B. Parker, Pharm.D.
Used with permission.
13.3.3 A sample of 15 patients suffering from asthma participated in an experiment to study the effect of
a new treatment on pulmonary function. Among the various measurements recorded were those of
forced expiratory volume (liters) in 1 second 1FEV 1 2 before and after application of the treatment.
The results were as follows:
Subject Before After Subject Before After
1 1.69 1.69 9 2.58 2.44
2 2.77 2.22 10 1.84 4.17
3 1.00 3.07 11 1.89 2.42
4 1.66 3.35 12 1.91 2.94
5 3.00 3.00 13 1.75 3.04
6 .85 2.74 14 2.46 4.62
7 1.42 3.61 15 2.35 4.42
8 2.82 5.14
On the basis of these data, can one conclude that the treatment is effective in increasing the FEV 1
level Let a = .05 and find the p value.
13.4 THE WILCOXON SIGNED-RANK
TEST FOR LOCATION
Sometimes we wish to test a null hypothesis about a population mean, but for some reason
neither z nor t is an appropriate test statistic. If we have a small sample 1n 6 302 from
a population that is known to be grossly nonnormally distributed, and the central limit theorem
is not applicable, the z statistic is ruled out. The t statistic is not appropriate because