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Chapter 13: Q3BSC (page 597)

Sign Test vs. Wilcoxon Signed-Ranks Test Using the data in Exercise 1, we can test for no difference between body temperatures at 8 AM and 12 AM by using the sign test or the Wilcoxon signed-ranks test. In what sense does the Wilcoxon signed-ranks test incorporate and use more information than the sign test?

Short Answer

Expert verified

The sign test uses only the signs of the differences, while the Wilcoxon signed-ranks test uses both the sign as well as the magnitude of differences.

Step by step solution

01

Given information

Samples are given showing the body temperature at 8 a.m. and 12 a.m.

02

Describe the sign test and Wilcoxon signed-ranks test

Both the Sign test and the Wilcoxon signed-ranks test are used to test the difference between temperatures.

In the Wilcoxon signed-rank test, ranks are used to assign the differences between the paired set of values. The Wilcoxon signed-ranks test uses both the sign as well as the magnitude of differences, whereas the sign test uses only the sign of the differences.

Thus, the Wilcoxon signed-rank test gives a more appropriate picture as it uses a decent amount of information.

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Most popular questions from this chapter

Crickets and Temperature The association between the temperature and the number of times a cricket chirps in 1 min was studied. Listed below are the numbers of chirps in 1 min and the corresponding temperatures in degrees Fahrenheit (based on data from The Song of Insects by George W. Pierce, Harvard University Press). Is there sufficient evidence to conclude that there is a relationship between the number of chirps in 1 min and the temperature?

Chirps in 1 min

882

1188

1104

864

1200

1032

960

900

Temperature\(\left( {^ \circ F} \right)\)

69.7

93.3

84.3

76.3

88.6

82.6

71.6

79.6

CPI and the Subway Use CPI/subway data from the preceding exercise to test for a correlation between the CPI (Consumer Price Index) and the subway fare.

Using the Wilcoxon Signed-Ranks Test. In Exercises 5鈥�8, refer to the sample data for the given exercises in Section 13-2 on page 611. Use the Wilcoxon signed-ranks test to test the claim that the matched pairs have differences that come from a population with a median equal to zero. Use a 0.05 significance level.

Exercise 6 鈥淪peed Dating: Attractiveness鈥�

Wilcoxon Signed-Ranks Test for Body Temperatures The table below lists body temperatures of seven subjects at 8 AM and at 12 AM (from Data Set 3 鈥淏ody Temperatures in Appendix B). The data are matched pairs because each pair of temperatures is measured from the same person. Assume that we plan to use the Wilcoxon signed-ranks test to test the claim of no difference between body temperatures at 8 AM and 12 AM.

a. What requirements must be satisfied for this test?

b. Is there any requirement that the samples must be from populations having a normal distribution or any other specific distribution?

c. In what sense is this sign test a 鈥渄istribution-free test鈥�?

Clinical Trials of Lipitor The sample data below are changes in LDL cholesterol levels in clinical trials of Lipitor (atorvastatin). It was claimed that Lipitor had an effect on LDL cholesterol. (The data are based on results given in a Parke-Davis memo from David G. Orloff, M.D., the medical team leader for clinical trials of Lipitor. Pfizer declined to provide the author with the original data values.) Negative values represent decreases in LDL cholesterol. Use a 0.05 significance level to test the claim that for those treated with 20 mg of Lipitor and those treated with 80 mg of Lipitor, changes in LDL cholesterol have the same median. What do the results suggest?

GroupTreatedwith20 mgofLipitor

-28

-32

-29

-39

-31

-35

-25

-36

-35

-26

-29

-34

-30


GroupTreatedwith80 mgofLipitor

-42

-41

-38

-42

-41

-41

-40

-44

-32

-37

-41

-37

-34

-31
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