Wilcoxon Mann-Whitney U Test

Graham Tall   G.E.Tall@bham.ac.uk

Reference: 
Siegel, S. Castellan, N.J.  (1988)  NonParametric Statistics for the Behavioural Sciences  London:McGraw-Hill

The Mann-Whitney U test is directly equivalent to the t test and the Analysis of Variance where there just two groups of individuals to be compared and the data is not related.  It should be used when the data is ordinal OR when the difference in standard deviation (F test) is so great that the groups cannot be considered as coming from the same population. 

The logic of the test is simple.  The scores of the two groups are placed in order and then ranked, as indicated below:

The total of the ranks of each group is then calculated:   

Total ranks of Group 1 = 3 + 4 + 7 + 9 + 10      = 34
Total ranks of Group 2 = 1 + 2 + 5.5 + 5.5 + 8  = 22
Total Group1 and Group2 = 34 + 22                  = 45

Since there are 10 numbers, the sum of the ranks of Group 1 and Group 2 should
equal   (10 ( 10 - 1 )) / 2 = ( 10 * 9 )/ 2 = 45   Which is the case.

If the total ranks of each group are similar, then the null hypothesis should be accepted.  If not, then check the tables in the appendices of Siegel to determine the probability level. 

Home Page    Research Introduction   Quantitative Advice    Index     Statistical Tests      Types of Number      Basic Statistics