What does U stand for in Mann-Whitney U Test? I can't seem to find the definition of "U" in any site.

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    $\begingroup$ It doesn't stand for anything. It is the name of the test statistic used to compare the samples under investigation. Like the t in t-test. The calculation for U is described on the wiki page $\endgroup$ – paqmo Oct 25 '16 at 12:45
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    $\begingroup$ This seems like a perfectly good question to me. $\endgroup$ – gung - Reinstate Monica Oct 25 '16 at 12:55
  • $\begingroup$ could it be possible that U stands for Unequal sample sizes because that is what Mann-Whitney tried to solve since Wilcoxon only considered equal sample sizes? $\endgroup$ – Dr.DOOM Oct 25 '16 at 13:04
  • $\begingroup$ @Dr.DOOM maybe, maybe not. While writing my answer I made few fast searches through books on history of statistics (via google scholar, google books and just searching the books) and didn't find much about the name of this test. $\endgroup$ – Tim Oct 25 '16 at 14:05

Anyone is allowed to give any possible name for the test statistic they design. Mann and Whitney (1947) decided to name the one they proposed as "$U$". In their paper they do not give any reasons why such name was chosen, but as from the very beginning of the text they compare their test to the one proposed by Wilcoxon (1945), named as "$T$", so I'd guess that they simply took the next letter from the alphabet... Wilcoxon does not give any reason for choosing "$T$", but I guess that the same as "$t$" in $t$-test it stands for "test". So it seems that statisticians are not very creative in choosing names for their inventions.

Mann, H. B., & Whitney, D. R. (1947). On a test of whether one of two random variables is stochastically larger than the other. The annals of mathematical statistics, 50-60.

Wilcoxon, F. (1945). Individual comparisons by ranking methods. Biometrics bulletin, 1(6), 80-83.

  • $\begingroup$ It looks as though, in that paper, Wilcoxon possibly meant T to stand for Total. About one third of the way down the second column on page 81 is a comment. $\endgroup$ – mdewey Oct 25 '16 at 14:42
  • $\begingroup$ @mdewey yes, but Mann and Whitney refer to it as T, so I guess the name was used like this when they were writing their paper. $\endgroup$ – Tim Oct 25 '16 at 14:42
  • $\begingroup$ $U$ stands for $u$nknown reason for this symbol. $\endgroup$ – Nick Cox Oct 25 '16 at 18:39
  • $\begingroup$ can you explain why "Unknown" $\endgroup$ – Dr.DOOM Oct 26 '16 at 6:22
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    $\begingroup$ I guess @NickCox was joking. $\endgroup$ – Tim Oct 26 '16 at 7:07

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