Editing Mann–Whitney U test (section)

====''ρ'' statistic====
A statistic called ''ρ'' that is linearly related to ''U'' and widely used in studies of categorization ([[discrimination learning]] involving [[concept]]s), and elsewhere,<ref name="H1976" /> is calculated by dividing ''U'' by its maximum value for the given sample sizes, which is simply {{math|1=''n''<sub>1</sub>×''n''<sub>2</sub>}}. ''ρ'' is thus a non-parametric measure of the overlap between two distributions; it can take values between 0 and 1, and it estimates {{math|1=P(''Y'' > ''X'') + 0.5 P(''Y'' = ''X'')}}, where ''X'' and ''Y'' are randomly chosen observations from the two distributions. Both extreme values represent complete separation of the distributions, while a ''ρ'' of 0.5 represents complete overlap. The usefulness of the ''ρ'' statistic can be seen in the case of the odd example used above, where two distributions that were significantly different on a Mann–Whitney ''U'' test nonetheless had nearly identical medians: the ''ρ'' value in this case is approximately 0.723 in favour of the hares, correctly reflecting the fact that even though the median tortoise beat the median hare, the hares collectively did better than the tortoises collectively.{{citation needed|date=February 2012}}