# Mann-Whitney U Test

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## Mann-Whitney U Test

The Mann-Whitney U test is a nonparametric version of the T-test, used to assess a null hypothesis; stating that all outcomes have an equal chance of being greater or lower than the other. The first idea of such a test was in 1914, however it wasn’t fully completed at this time. In 1945, Frank Wilcoxon proposed a more in-depth view however, it was still missing some key points. A few years after in 1947, Henry Mann and his student Donald Whitney conducted a full analysis and created what is now known as the Mann-Whitney U test.

A common way to conduct a Mann-Whitney U test is to first decide on a null and alternative hypothesis; for example, ‘There will be no difference between the speed of a dog and the speed of a cat’, ‘There will be a difference between the speed of a dog and the speed of a cat’. To test these hypotheses, a test using six cats and six dogs will take place, where each animal will race the same distance on the same track. The times of all 12 animals are recorded and each animal will be given a score based off how many of the other animal they beat. The results could be in this order: C, C, D, C, D, D, D, C, D, D, C, C with ‘C’ being cat and ‘D’ being dog. The cats’ scores were: 6, 6, 5, 2, 0, 0; with the dogs’ scores being 4, 3, 3, 3, 2, 2. The next stage is to add up all the scores for each animal (cat – 6+6+5+2+0+0=19) (dog – 4+3+3+3+2+2=17). This study shows that, although not much, there is a difference between the speed of a dog and the speed of a cat.

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