# [EpiData-list] Asymmetric limbs of Confidence Interval - clarification

epidata-list at lists.umanitoba.ca epidata-list at lists.umanitoba.ca
Wed Feb 16 08:34:33 CST 2011

```The statistical principles for Confidence intervals for proportions are
several as Jamie Hockin indicated. The strategy of Openepi (and formerly
in Epi6 also created by Andrew  Dean) was in several commands to show a
number of these such that it is up to the user to decide which of the
principles is the optimal for a given estimation.

Usually the methods will in a simplified manner be one of these three:
a. Some sort of normal approximation method - these tend to give
symmetrical intervals around the point estimate
b. Exact ones based on resampling and cut off point's for probabilities
among the sampled estimates.
c. Enhanced approximative methods often based on non-parametric
principles, that is some sort of ranking.

Current implementation in EpiData can be any of a b c, but for small
samples would either be b (tables, life tables) or c (proportions).

My intention would be to include all of the estimations for simple
situations as described by Altman et al, currently this has been done
for proportions and life tables. I suggest that users read the book:
Altman et al. Statistics with confidence, London, BMJ books. ISBN 0 7279
1375 1, 2nd edition,2005. For proportions this is given on p 47 and life
table methods on p 94. This is also found in the documentation for
Analysis (press F1 when analysis is running).

In the book Altman et al compares for several measures the standard
approximative methods (a above) with the enhanced ones (c above). For
proportions the problem is that the symmetrical (standard) methods can
give proportions below 0 or above one, whereas the enhanced one
implemented will not do so.

In papers the reference for the CI would be Altman et al as implemented
in EpiData Analysis.

Jamie's offer to assist in writing guidance on this is definetely
welcomed and encouraged.

Regards
Jens Lauritsen

> In most situations, the differences will not be important. However, when working with small numbers as in many outbreaks, the "exact" CI may be preferred. Certainly, a short document on statistical methods employed will be useful. I'm happy to help write that.
>
> Jamie
>
> On 2011-02-16, Ajay wrote:
>> Query - why are the two limbs of the confidence interval [about a proportion] different?
>

```

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