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I just want to know.. Where does the "12" in the Kruskal Wallis formula comes from? I hope someone can give me a very good explanation.

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    $\begingroup$ $12$ comes from the fact that $\sum_{i=1}^N (i - \frac{N+1}{2})^2 = \frac{(N-1) N (N + 1)}{12}$, so it occurs naturally in the expression for the sample variance of the ranks of the outcomes which is (deterministically) equal to $\frac{N (N + 1)}{12}$. $\endgroup$ – guy Jun 10 '16 at 14:40
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"The sum of the first N integers is 1/2*N(N+ 1) and the sum of their squares is 1/6*N(N+ 1)(2N+ 1). It follows that the mean and variance of the first N integers are 1/2(N+1) and 1/12*(N^2-1)."

This is where the 12 appears first in William H. Kruskal and W. Allen Wallis: Use of Ranks in One-Criterion Variance Analysis, Journal of the American Statistical Association, Vol. 47, No. 260 (Dec., 1952), pp. 583-621

I suppose you read more on that in http://www.jstor.org/stable/pdf/2280779.pdf

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