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Mann Whitney Test (Wilcoxon Rank Sum)

The Mann Whitney test is the nonparametric version of the two sample t-test; it compares the means of two samples. It tests the hypothesis:

H0 the samples are drawn from populations with equal means
H1 the mean of the population of sample 'm' is [less than/greater than/not equal to] that of sample 'n'

It is similar in concept to the Wilcoxon Signed Rank Test and is also known as the Wilcoxon Rank Sum Test. The test involves:

• sort the combined results into size order and allocate ranks
• find the sum 'w' of the ranks of the sample with the smallest number of values (if they both have the same number of values, select either). This is one of the critical values.

For small data sets the critical value is found from published tables. Because the sum of the ranks must be an integer, it is not usually possible to find the exact critical value:

 or

 m number of values in the sample with the least number of values n number of values in the other sample μ 1 the mean of the sample containing the smallest number of values

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