# st: RE: Different confidence intervals from proportions and tabulates (also in survey)

 From "Nick Cox" To Subject st: RE: Different confidence intervals from proportions and tabulates (also in survey) Date Sun, 29 Oct 2006 22:55:15 -0000

```The example code you give does not give
any instances with lower confidence limits
below zero, which I assume is what you mean
by negative confidence intervals. But clearly
the CIs do differ.

Setting aside the complications of -svy-, which
is naturally a big set-aside:

There is no carved on stone, handed down from
on high, method of getting "CORRECT" [your word] binomial
confidence intervals. This is why -ci- (pure
and simple) offers a variety of ways of doing it,
and what you get over a range of real situations is
interestingly scary. Sometimes methods agree nicely;
other times they don't. Also, sometimes a confidence level
means about that much coverage, but often not.
The manual entry for [R] ci gives one entry into
the literature. The paper by Brown and friends in
Statistical Science 2002 is relatively friendly,
and likely to be web-accessible to you.

Regardless of that, as proportions approach 0
(or 1, really the same problem, modulo some measurement
convention), then on any reasonable view the problem becomes
increasingly asymmetric, and thus not best to be thought
in terms of

estimate +/- some multiple of standard error,

which, whatever they may say in introductory treatments,
is at best a crude approximation to what is going on.
A much better scale to work on is logit.

Thus negative confidence limits
are in essence a clear sign that you are using
an inappropriate method, and/or that a one-sided
interval would be more appropriate.

Nick
n.j.cox@durham.ac.uk

Jason Ferris
>
> I have been running survey proportions and observing results with
> negative confidence intervals (which doesn't make sense).  When I use
> survey tab (with column percent, se and ci) I get the same point
> estimates and standard errors but different 95% confidence
> intervals.  I
> assume this is an issue with the proportion calculations
> using "Binomial
> Wald" for confidence intervals.
>
> I checked the survey manual and have not been able to find why:
>
> Paste the following command to see my dilemma:
> webuse nhanes2b, clear
> svy: proportion race
> svy: tab race, ci se
>
>
> The results show the same point estimates and standard errors (with
> rounding) but different CI's.  As mentioned, for my data, I get some
> negative CI's for svy: proportions commands but not for the svy:
> tabulate commands. My ultimate concern is being able to automatically
> extract the CORRECT estimates to excel (from using matrix
> e(b) and e(V)
> - and calculating 95% CI from square-root of e(V) *1.96).
>
> I am using the latest version of Stata 9.2, on Windows XP.

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