Re: Estimation of variance of proportions

=?UTF-8?Q?Jean-No=C3=ABl?= <aubertot@xxxxxxxxxxxxxxx> wrote in
news:11931925.1151133920157.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxx:

Hi everyone,
I would like to estimate the variance of estimated proportions. I
think that it is generally correct to estimate the variance by
VAR^=np^(1-p^), where p^ is the estimated proportion and n the sample
size. However, when p^=0, this leads to an estimated variance VAR^=0,
which puzzles me because the variance does not depend anymore on n. It
is quite different to obtain p^=0 with n=2, or with n=100000 for
instance. Does anyone know how to estimate the variance of a
proportion when the estimated proportion is null ?

Thank you in advance for your help.

JN


If you _know_ that p or (1-p) is zero, then the variance _is_ zero. If you
do not know that p=0, then why would you torture the formula into giving
you a meaningless estimate?

If you think that the proportion of successes, hits or events is not
necessarily zero, then you should not use zero, but rather a small non-zero
estimate. In that instance, the Poisson distribution and associated methods
might be mathematically convenient. The variance of the Poisson equals the
expected value which is np. The reasonableness of the Poisson approximation
(with large n) to the binomial is easy to see, since np(1-p) will approach
np because (1-p) is near 1.

--
David Winsemius
.

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