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 From: Jason Stover Subject: Re: casereader numbering Date: Tue, 22 Jul 2008 11:25:36 -0400 User-agent: Mutt/1.5.18 (2008-05-17)

```On Tue, Jul 22, 2008 at 07:44:47PM +0800, John Darrington wrote:
> On Thu, Jul 17, 2008 at 03:18:33PM -0400, Jason Stover wrote:
>
>      This would be valuable for other procedures, too. Anything that
>      could use permutations could make use of such a function. Also, it
>      would be useful for bootstrap and jacknife tests.
>
>
> How would  numbering the cases will help for those applications?  I
> would have thought that some kind of random/low discrepency sequence
> iterator would be required.

I hadn't thought it through entirely when I typed that, but
permutation tests can be done by generating a random permutation p(1),
p(2), ..., p(n); then instead of computing a statistic from the data
T(X_1, X_2, ..., X_n), we compute T(X_{p(1)},
X_{p(2)},...,X_{p(n)}). Do that for many random permutations and check
how far away the original statistic is from its parameter under the
null hypothesis. "How far" is measured by looking at distances of the
statistics from the permuted data.

In the past, I usually did this in C by generating a random permutation,
then doing something like:

for (i = 0; i < n; i++)
{
y[i] = x[p[i]];
}
t[i] = T(y);

(That bit about computing T(y) is usually more complicated.)

So that's what I was thinking. Having case numbers may not be useful
for permutation tests if we aren't going to just copy data into an
array, but I thought it might be, even if I couldn't see the details