Hello, in a reference book on applied statistics about Mann Whitney u test, there is an expression as follows
"dependent numerical variable must have same distribution on groups (categories)"
Should i check distribution before applying Mann w. u test.?
thnx on advance
best regards
There is no general answer to this question, because it depends on what hypothesis you want to test.
The U-test test "stochastic equality", and for this is makes no assumptions about the distribution. If the test should be about a "location shift", then the distributions must have the same shapes (same variance, skew, kurtosis etc.; so that the location is the only property that is allowed to differ between the distributions).
The unpleasant fact is that it is very hard to see if distributions differ only ba a location shift. If you would have enough data to see this, then you have enough data to efficiently test the location shift using a t-test.
There is no need. It is when the assumptions of the independent samples t-test are not met that you make use of the non-parametric version of t-test, which is Mann-Whitney U test.
That is the reason non-parametric tests are usually called distribution free tests because they make no assumption about the underlying distribution.
No, Peter Koleoso , the U-test is not just the "non-parametric version of t-test". This statement is true only under very specific assumptions, and these are usually drastically violated when people think about the fact that a t-test might not be appropriate. Your statement that non-parametric tests "make no assumption about the underlying distribution" is correct but is completely misses the point (it is not a justification that a U-test would be a valid substitute for a t-test). When the U-test should serve as a substitute for the t-test, the assumption is that the distributions in both groups must be equal in all aspects except location. I have not encountered a situation where this assumption would be reasonable.
If X and Y are two continuous random variables, then Mann-Whitney U test essentially tests the hypothesis H0: P[X>Y]=0.5 vs. H1: ~H0. It doesn't need the distribution family of X and Y to be the same.
However, if X and Y happen to have the same distribution except for the location (median), then Mann-Whitney U test can tell whether they have the same median or not.
So if you are not testing equality of medians, the answer to your question is NO.
FYI, a citation for Jochen Wilhelm's answer (should you need one) can be found in Sheskin's Handbook of Parametric and Nonparametric Statistical Procedures (1997, ISBN 0-8493-3119-6) on page 181, where there is a rich discussion of its use. Hope this is helpful to your work.
Rich
- Badges
- Science topic
- Similar topics
- Correction