# Mann Whitney u test- Interpretation help?

#### Pippy

##### New Member
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
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
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
Hi,

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.