# How to report asymmetrical confidence intervals of a proportion?

I've calculated the proportion of chicks fledged out of the number of eggs hatched in each year using prop.test() in R. I see that it gives me the proportion fledged, but also the 95% confidence interval, which is what I'm after. Having read the excellent information from another question on this site here, I understand why I don't have symmetry in my 95% CIs!

• However, how should I report this in a paper?

I've seen people report values as 38% (±0.2%), with an indication that the value in brackets is 95% CI. Obviously this won't work for asymmetrical CIs. Must I report the upper and lower values in these cases?

• Sure, I would report the lower and upper limit. For a real-world example, see this BMJ article (p. 4, Table 2). May 31, 2011 at 1:08
• Thanks @Bernd. That's a great paper that provides a great solution.
– Mog
May 31, 2011 at 2:00

You should report the lower and upper intervals and also the method used to calculate the interval.

It turns out that there is no 'right' way to calculate confidence intervals for proportions, but instead many competing methods, each with advantages and disadvantages. The lack of a universally correct method stands in contrast to many statistical things that you might put numbers to, like means and standard deviations. For your interval to be fully specified you have to say how you calculated it.

• Thanks @Michael. That's good to know that the method should be reported as well. So, if I'm using the prop.test() code in R, based on the other (linked) answer, I would be using the Wilson method with Yates' continuity correction, correct? Is there a reason why I should or shouldn't use the continuity correction?
– Mog
May 31, 2011 at 2:06
• @Mog You've asked a sensible question that is surprisingly difficult to answer (at least, to answer briefly). Wilson's method allows the local interpretation of "What are the chances that the true proportion in this case is within this interval?" in that it approximates both a Bayesian credible interval with a uniform prior and a Fisher fiducial interval. However, if you apply a continuity correction to make it behave more like a Clopper-Pearson interval then that interpretation is lost. In my opinion Wilson's intervals are excellent, without the 'correction'. Jun 1, 2011 at 2:56