*Dear Professor Mean, I found a journal article with a confidence interval that was asymmetric. For example, the authors reported a mortality difference of 5% and a 95% confidence interval of -1.2% to 12%. I can’t understand how the CI can be unequally distributed if it uses the form ESTIMATE +/- 1.96 * STANDARD ERROR.
Not every confidence interval uses a plus or minus type formula. The ones that don’t are usually asymmetric. In particular, most confidence intervals involving ratios are asymemmetric (though some of them are symmetric on a log scale). Also confidence intervals that take the small sample sizes into account are often asymmetric. It’s good that you remember your confidence interval formula from your Statistics class, but your instructor probably didn’t have time to show you every possible confidence interval formula.
You can find an earlier version of this page on my original website.