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Chapter 13: Q1BSC (page 597)

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�?

Short Answer

Expert verified

a. The requirement for conducting a Wilcoxon signed-ranks test is that the samples should be simple random samples, and the distribution of the population of difference should be symmetric.

b. No, there is no requirement for the populations of the given samples to follow a certain distribution like normal distribution or any other distribution.

c. Since there is no strict requirement for the populations to follow a particular distribution, the sign test can be regarded as the 鈥渄istribution-free test鈥�.

Step by step solution

01

Given information

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

02

Define Wilcoxon signed-ranks test

The Wilcoxon signed-ranks test is a non-parametric test that can be used to test the claim of no difference in the values of the two samples using ranks.

03

Requirements of the Wilcoxon signed-ranks test

a.

The following are the requirements for conducting a Wilcoxon signed ranks test:

  • The sample data should be a simple random sample.
  • The population of the differences of the values between the two samples should follow a symmetric distribution.

b.

Since thetest is distribution-free, there is no requirement for the populations of the samples to follow a specific distribution such as the normal distribution or any other distribution.

c.

Since there is no assumption regarding the distribution of the populations from which the samples have been taken,this sign test can be regarded as a 鈥渄istribution-free test鈥�.

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Most popular questions from this chapter

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

Using the Kruskal-Wallis Test. In Exercises 5鈥�8, use the Kruskal-Wallis test.

Correcting the H Test Statistic for Ties In using the Kruskal-Wallis test, there is a correction factor that should be applied whenever there are many ties: Divide H by

\(1 - \frac{{\sum T }}{{{N^3} - N}}\)

First combine all of the sample data into one list, and then, in that combined list, identify the different groups of sample values that are tied. For each individual group of tied observations, identify the number of sample values that are tied and designate that number as t, then calculate\(T = {t^3} - t\). Next, add the T values to get\(\sum T \). The value of N is the total number of observations in all samples combined. Use this procedure to find the corrected value of H for Example 1 in this section on page 628. Does the corrected value of H differ substantially from the value found in Example 1?

Nominal Data. In Exercises 9鈥�12, use the sign test for the claim involving nominal data.

Births A random sample of 860 births in New York State included 426 boys and 434 girls. Use a 0.05 significance level to test the claim that when babies are born, boys and girls are equally likely.

Odd and Even Digits in Pi A New York Times article about the calculation of decimal places of\(\pi \)noted that 鈥渕athematicians are pretty sure that the digits of\(\pi \)are indistinguishable from any random sequence.鈥� Given below are the first 25 decimal places of\(\pi \). Test for randomness in the way that odd (O) and even (E) digits occur in the sequence. Based on the result, does the statement from the New York Times appear to be accurate?

1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3

Test for Normality Use the departure delay times for Flight 19 and test for normality using a normal quantile plot.
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