Mann-Whitney U Test
{From the Institute of Phonetic Sciences (IFA): http://www.fon.hum.uva.nl/}

The Mann-Whitney U test is used to analyze rank-ordered data. This test is a nonparametric alternative to the independent-sample, Student t test, and yields results identical to those obtained from the Wilcoxon Two Independent Samples Test.

H₀: 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 Mann-Whitney statistic, N₁ and N₂ are the number of cases in samples 1 and 2, respectively, and R₁ is the sum of the ranks for the first sample.

Group 1		Group 2
Score	Rank		Score	Rank
22	17		17	6.5
25	19.5		13	1.5
25	19.5		19	11.5
19	11.5		14	4.5
19	11.5		17	6.5
21	16		15	5
19	11.5		13	1.5
20	14.5		18	8.5
24	18		14	4.5
			20	14.5
			18	8.5

For this example N₁ = 9, and N₂= 11. The sum of the ranks (R₁) 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 Mann-Whitney U Test, where we learn that the probability of a U of 5, under the null hypothesis, when N₁ = 9, and N₂= 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