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## Re: new algorithm for wilcoxon signed-rank test

**From**: |
Jason Stover |

**Subject**: |
Re: new algorithm for wilcoxon signed-rank test |

**Date**: |
Fri, 6 Feb 2009 16:22:45 -0500 |

**User-agent**: |
Mutt/1.5.18 (2008-05-17) |

On Wed, Feb 04, 2009 at 10:15:26PM -0800, Ben Pfaff wrote:
>* Here's an explanation.*
...
>* Notably, these trivial cases include all values of W for N = 1.*
>* *
>* Now consider the remaining, nontrivial cases, that is, N > 1 and*
>* 1 <= W <= N*(N+1)/2. In this case, apply the following identity:*
>* *
>* S(N,W) = S(N-1, W) + S(N-1, W-N).*
>* *
>* The first term on the right hand is the number of subsets that do*
>* not include N that sum to at least W; the second term is the*
>* number of subsets that do include N that sum to at least W.*
>* *
>* Then we repeatedly apply the identity to the result, reducing the*
>* value of N by 1 each time until we reach N=1. Some expansions*
>* yield trivial cases, e.g. if W - N <= 0 (in which case we add a*
>* 2**N term to the final result) or if W is greater than the new N.*
Simple and clever. I think you should publish this. I'm not surprised
it hasn't been used in statistical software before. Most people in the
field of non-parametric statistics don't think about algorithms from
discrete math.
It's a good result, especially for a sleepless night's work.
-Jason