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746 CHAPTER 13 NONPARAMETRIC AND DISTRIBUTION-FREE STATISTICS
5. Describe a situation in your particular area of interest where each of the following tests could be
used. Use real or realistic data and test an appropriate hypothesis using each test.
(a) The sign test
(b) The median test
(c) The Wilcoxon test
(d) The Mann–Whitney test
(e) The Kolmogorov–Smirnov goodness-of-fit test
(f) The Kruskal–Wallis one-way analysis of variance by ranks
(g) The Friedman two-way analysis of variance by ranks
(h) The Spearman rank correlation coefficient
(i) Nonparametric regression analysis
6. The following are the ranks of the ages (X ) of 20 surgical patients and the dose (Y ) of an analgesic
agent required to block one spinal segment.
Rank of Rank of Dose Rank of Rank of Dose
Age in Requirement Age in Requirement
Years (X ) (Y) Years (X ) (Y )
1 1 11 13
2 7 12 5
3 2 13 11
4 4 14 16
5 6 15 20
6 8 16 18
7 3 17 19
8 15 18 17
9 9 19 10
10 12 20 14
Compute and test (two-sided) for significance. Let a = .05. Determine the p value for this test.
r s
7. Otani and Kishi (A-12) studied seven subjects with diabetic macular edema. They measured the
foveal thickness 1mm2 in seven eyes pre- and post-unilateral vitrectomy surgery. The results are
shown in the following table:
Subject Pre-op Foveal Thickness (Mm) Post-op Foveal Thickness (Mm)
1 690 200
2 840 280
3 470 230
4 690 200
5 730 560
6 500 210
7 440 200
Source: Tomohiro Otani, M.D. Used with permission.
Use the Wilcoxon signed-rank test to determine whether one should conclude that the surgery
is effective in reducing foveal thickness. Let a = .05. What is the p value