Question

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

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

Given information

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

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.