Mann-Whitney U Test

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