sleszyk wrote:
> I have another question about the proportion confidence interval:
>
> With the above formula one can calcute the symmetrical interval, which is ok
> as long as the proportion is not too close to 0 or 1.
> However, from what I've heard the "real" CI is always asymmetrical (well,
> maybe except for p=0,5).
A CI is any interval computed by a technique that gives the specified
coverage probability. It can be symmetric (most usual), one-tailed
(useful in some specialized situations but usually NOT for research
purposes), or asymmetric two-tailed. Roughly, these correspond to the
many ways in which one can pick an interval under the normal curve that
represents 95% of the area. (Indeed, we can get some truly perverse
confidence _regions_ consisting *only* of the tails... it is provable
that these are worse, by any reasonable criterion, than the interval
estimators, but this result, while easy, is not by any means trivial.)
What you may have heard - and it is true - is that the minimum-width CI
is asymmetric. This is often true (eg, for a proportion with P <> .5),
though the improvement is rarely worth the messier algebra. It is also
true that a Bayesian or likelihood interval is often asymmetric.
-Robert Dawson
.
.
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