I want to use the Whitney Mann U test (i.e. Wilcoxon Rank Sum) test to test for differences in an ordinal outcome variable (say a 5 point Likert item) among two randomly selected samples. I've read a few articles online and I'm not sure what challenges are introduced when the data are in fact ordinal. Hopefully you all can help me understand the implications of working with ordinal data.
- Comparing two samples.
- The two groups of data are independent.
- The type of variable could be continuous or ordinal.
- The data might not be normally distributed.
However, a STA3024 file hosted by the stats department at UFL, a STAT464 page hosted by the stats department at PennState, a STAT105 file hosted by the stats department at UCLA, and an article hosted by the stats department at Iowa -- Ames claim this test is only appropriate for observations drawn from continuous distributions. How does the actual discrete reality of an ordinal sample affect the validity (and hypotheses) of this test (if at all)?
While the UFL file claimed continuity was important, it goes on to show an example of the Wilcoxon Rank Sum test (i.e., the Whitney-Mann U test) using responses that fall on a 5 point Likert scale. In fact, it argues that using this test with ordinal data is reasonable since the WMU test "uses only the order of the responses, not their actual values." What is happening with these data and this test to make this valid?