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I've recently begun learning the Mann-Whitney U test and have had to use normal approximation. The formula is straight forward, but I find myself wondering why you use 12 as the denominator in the square root portion. I enjoying knowing where numbers come from where possible, especially when they are a very unusual number like 12. I attempted to google around to find the answer, but all I could find was places that could tell me the formula but not the WHY behind it.

Toast
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  • Just a thought: ranks are uniformly distributed, and the variance for a standard (0,1) uniform distribution is $\frac 1{12}$ – jameselmore Jan 07 '16 at 15:24
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    I really don't know (I am totally stupid in the area of statistics - as well as in many other). I just want to congratulate you for asking such a question : this is avery good attitude. Go on that way and you will have a great future ! $+1$ – Claude Leibovici Jan 07 '16 at 15:27
  • jameselmore: After searching based on what you said, it appears to be the case. I admit I don't fully understand it right now, but that gives me a good place to start. Thank you. – Toast Jan 07 '16 at 15:55
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    Claude Leibovici: Thank you! I don't like to just blindly apply numbers and concepts to things. – Toast Jan 07 '16 at 15:55

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