MannWhitney U Test
{From the Institute of Phonetic Sciences (IFA):
http://www.fon.hum.uva.nl/}
The MannWhitney U test is used to analyze rankordered data. This test is a nonparametric alternative to the independentsample, Student t test, and yields results identical to those obtained from the Wilcoxon Two Independent Samples Test.
H_{0}: The populations from which the two samples are taken have identical median values. To be complete, the two populations have identical distributions.
Assumptions:
None that matter.
Scale:
Ordinal.
Procedure:
Rank the combined set of data from the two groups from
lowest to highest with tied scores receiving a rank equal to the average
position of those scores in the ordered array (see the example). Compute
where U is the MannWhitney statistic, N_{1} and N_{2} are the number of cases in samples 1 and 2, respectively, and R_{1} is the sum of the ranks for the first sample.

For this example N_{1} = 9, and N_{2 }= 11. The sum of the ranks (R_{1}) is 139. Substituting these values into the equation given above yields:
U = (9 x 11) + [ 9(9 + 1) / 2 ]  139
= 99 + (9)(10)/2 139
= 99 + 45  139
= 5
We can compare this value to the Critical Values given in Tables of Critical Values for the MannWhitney U Test, where we learn that the probability of a U of 5, under the null hypothesis, when N_{1} = 9, and N_{2 }= 11 is less than .01. We conclude that the groups are significantly different.
If you have already computed U and want to determine its level of significance, click here: HERE