There are two different types of Wilcoxon tests for two different types of studies. The reason these tests are important is because they require less assumptions to be made about the data and so the tests will be work well for studies with very small sample sizes. If you can make more assumptions about the data you will get more accurate results and so these tests are not usually used in studies with large sample sizes.
1. Wilcoxon Signed Rank Test
This test is a one sample test which is used to compare a difference of two measurements in one population.
Example: In a study of ten patients, all of whom are given drug A, the investigator wants to look at the difference between blood pressure measurements before and after treatment.
2. Wilcoxon Rank Sum Test (Also known as the Mann-Whitney Test)
This test is a two sample test for continuous outcomes. This is when you have an outcome you want to compare in two populations or when you have one population but individuals are assigned to one of two treatments and you want to compare an outcome between the two treatment groups.
Example: Twelve patients, six women and six men, have all been given drug A, the investigator is interested in comparing to see whether the blood pressure change is different for men and women.
Example: In a study of seven patients, patients are randomized to drug A or drug B. The investigator wants to see if the change in blood pressure is different for the individuals who were given drug A as compared to the individuals who were given drug B.
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