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

 From: John Darrington Subject: Re: new algorithm for wilcoxon signed-rank test Date: Thu, 5 Feb 2009 16:16:29 +0900 User-agent: Mutt/1.5.13 (2006-08-11)

```I think it's quite amazing!  I remember thinking when I first put that
routine into pspp, that there was some redundant calculations here,
but then thought that if there was a better way somebody would have
already come up with it ...

One small point about the implementation: It seems that array[0] is
never used.  So it count be one int smaller.

J'

----- Forwarded message from Ben Pfaff <address@hidden> -----

...
Actually, here's a solution that is even better.  A test program using it
calculates (correctly) and prints *all* the values for 1 <= N <= 30, 1 <=
W <=
N*(N+1)/2, in under .2 seconds *total*.

The runtime of this algorithm is O(N*W) and it uses O(W) space.

int ranksum6(int N, int W)
{
int *array;
int max;
int total;

assert (N >= 0);

if (N == 0)
return 0;
else if (W <= 0)
return 1 << N;
else if (W > N * (N + 1) / 2)
return 0;
else if (N == 1)
return 1;

array = calloc (sizeof *array, W + 1);
array[W] = 1;

max = W;
total = 0;
for (; N > 1; N--)
{
int max_sum = N * (N + 1) / 2;
int i;

if (max_sum < max)
max = max_sum;

for (i = 1; i <= max; i++)
if (array[i] != 0)
{
int new_W = i - N;
if (new_W <= 0)
total += array[i] * (1 << (N - 1));
else
array[new_W] += array[i];
}
}
total += array[1];
free (array);
}

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```

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