On Wed, 21 Jun 2000, Dale Berger wrote:
> Yet, p=0 is a special case where an outcome is impossible. A
> reasonable confidence interval for p should not include zero if the
> outcome has been observed in a sample. Not so?
I am unable to reconcile this assertion with the fact that the only
values one can observe, in the vicinity of (some small) p, are 0/n,
1/n, 2/n, ... ; and that if 1/n is observed, 0/n is possible to have
observed, in which case one's estimate of p would, presumably, have
been 0, at least to the precision available in the data.
Possibly the dissonance arises from a (as it were) theological
interpretation of "impossible", and the fact that p cannot be
observed directly (one can only observe k instances, and relate that
to the n potential instances); possibly it turns on something rather
more mundane, such as the precision with which one is estimating p,
which is necessarily finite. (One thinks of those computer programs
that cheerfully report p = 0.0000 in connection with a statistical
test.)
-- Don.
------------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-471-7128
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