Confidence intervals exceeding 100% and going below 0% for mortality rates


This is probably a very naïve question however, when plotting some graphs of mosquito mortality against different insecticide treatments I noticed the confidence intervals for some of the most effective treatments exceed 100% and that in the control they sometimes go below 0%. Firstly, I don't like having to include values over 100% and below 0% on a graph axis which is supposed to be displaying mortality. Secondly, I wondered if it possible for CI values to fall outside of a normal 0-100% range?

Thanks :)


TS Contributor
It sounds like you may be using confidence intervals for interval data rather than binomial confidence intervals for proportions

Interval data are not bounded by 0 or 1.
I guess that you (or your software) are using the usual normal approximation for the estimated proportion, like giving a confidence interval for the proportion of 9 out of 10. (So 9 events happened out of n=10 trials). Then, if the number of trial are large then the proportion will be approximately normal. But if n is small and the proportion is close to 1 or 0 the interval will cross 1 or 0 like in this example:

 c(0.9 - 1.96*sqrt(0.9*0.10/10), 0.9 + 1.96*sqrt(0.9*0.10/10))
[1] 0.7140581 1.0859419
So here the upper interval is 1.08, which is to high. Of course the correct interval can not be larger than 1.

The easiest thing to do would be to simply set the highest interval to 1 (or to 0). Maybe it is not worth the effort to do an exact confidence inteval based on the binomial distribution (and not on the normal approximation).

Other intervals have been suggested like Clopper-Pearson or Agresti-Coull.