The Rank-Sum test

When the assumptions of the t-test are not met, the Rank-Sum test is often a good non-parametric alternative test. While the t-test can be used to test for the difference between the means of two distributions, the Rank-Sum test is used to test for the difference between the locations of two distributions. This difference in the test utility is due to the lack of parametric assumptions in the Rank-Sum test. The null hypothesis of the Rank-Sum test is that the distribution underlying the first sample is the same as the second sample. If the sample distributions appear to be similar, this allows us to use the Rank-Sum test to test for the difference in the locations of the two samples. As stated, the Rank-Sum test cannot specifically be used for testing the difference between means because it does not require assumptions about the sample distributions.

The test statistic procedure

The test procedure is straightforward. The process is outlined here and an example...