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Mann-Whitney-Wilcoxon Test

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Definition

The nonparametric version of the two-independent Samples t-test. It evaluates the equality of the Medians of two independent groups. Also called Mann-Whitney or Wilcoxon Rank Sums Test. Although it does not require a distribution to be specified for the sample data, it does make the assumptions of continuous measurements and independent Samples.

Application

Either of two complementary test statistics may be used. The Mann-Whitney 'U' statistic is the number of observations in the larger sample, say sample 2, that are smaller than each of the observations in the smaller sample, say sample 1. Alternatively, the observations in the two samples are pooled and ranked in ascending order, with equal ranks assigned to tied values. Then the Wilcoxon Rank Sum statistic, T+ is the sum of the ranks in sample 1 (the smaller sample). The two statistics are related by the equation:
U = n1n2 + n1(n1+1)/2 - T+