Question

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 “Body 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 “distribution-free test”?

Short answer

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 “distribution-free test”.

Step-by-step solution

Given information

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

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.

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 “distribution-free test”.