Hart differences in spread can be important Mann - Whitney test is not just a test of medians
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Nonparametric Tests of Differences in Medians: Comparison of the Wilcoxon–Mann–Whitney and Robust Rank–Order Tests
The nonparametric Wilcoxon–Mann–Whitney test is commonly used by experimental economists for detecting differences in central tendency between two samples. This test is only theoretically appropriate under certain assumptions concerning the population distributions from which the samples are drawn, and is often used in cases where it is unclear whether these assumptions hold, and even when they...
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