Mann Whitney u test- Interpretation help?

Pippy

New Member
#1
Hi

I have conducted a Mann Whitney u test to test to see if there is a difference between one of my variables and gender. The test shows there is a statistically significant difference. To determine where the difference lies do I just consult the mean rank score or the mean? Can I work out the percentage between the two mean scores to give me a percentage of difference or does it not work like this? Thanks for your help.
 

gianmarco

TS Contributor
#2
Hi,
there are many earlier thread on M-W test. But, before going on in replying, can you explain to us what the reason was of your choice of MW instead of t-test?

Regards
Gm
 

Pippy

New Member
#3
Hi GM

The data i have is ordinal data and therefore i choose Mann Whitney as its the non-parametric test so fits in with my data. I have had a little look at previous posts on here regarding M-W tests however my main question is just about determining significance of direction and wether i can convert this into a percentage difference so couldnt find any previous posts that answered this question. Thanks for your help.
 

gianmarco

TS Contributor
#4
Hi,
sorry for the delayed reply.

To determine where the difference lies do I just consult the mean rank score or the mean?
Mann-Whitney is usually held to test for the difference in median values between the two samples being considered. For this very reason, some statpacks provide (as far as I have seen around) a confidence interval for the difference in medians, along with MW statistics and p value.

The complicating factor is (at the best of my knowledge, but other stat guys here can correct me or put it in a more formal phrasing) that MW can be interpreted in different ways, depending on the assumptions you start from. This is explained rather well on Wikipedia.
In other words, a more general (and less stringent) formulation is that you are testing the degree to which
Under the null hypothesis, the distributions of both groups are equal, so that the probability of an observation from one population (X) exceeding an observation from the second population (Y) equals the probability of an observation from Y exceeding an observation from X, that is, there is a symmetry between populations with respect to probability of random drawing of a larger observation
Another formulation is that you are willing to test a difference in median. In this case (as far as I have understtod it), some assumptions need to be met, i.e. both samples with similar shape. Otherwise, MW could be sensible to a difference in shape even if the medians are equal. This latter case is explained here.

As for your question:
Can I work out the percentage between the two mean scores to give me a percentage of difference or does it not work like this?
I do not well understand you. Are you asking about some sort of confidence interval for the difference in median, or in score?
If you are happy with the second above point (i.e., similar shape; then you detect a shift in median values), you could (in my opinion) report the difference in median, along with the confidence inteval provided by statpacks, and then report the test statistics (i.e., U) and the associated probability (p).

Otherwise, if you are happy with the first above point (i.e., more general formation) you could report the test statistics and p value, and also report the "probability of superiority" (here explanation).

Hope this helps
Kind Regards
Gm