# How to decide and calculate the skewness of an asymmetric confidence interval around a mean or a mean difference?

I wonder how statistical programs decide to skew the confidence interval? (I mean the confidence intervals for the means, or for the mean differences).

How do they decide on the extent of this (without any bootsrapping)? I know they do it based on the skewness of the sample distribution (in two-tailed tests), but would appreciate any details on that.

• Can you give an example of what kind of interval you mean? Apr 25, 2014 at 13:11
• A simple 95% confidence interval, computed by the software for the mean errors after calculating a paired t-test. So the mean error means the mean of all X1 values - all X2 values.
– Vic
Apr 25, 2014 at 13:24
• A confidence interval based on a paired t-test should be symmetric. Can you show an example of an asymmetric interval for that case? When you say "the software", do you mean some software in particular? Apr 25, 2014 at 13:27
• I am looking at a paper full of asymmetric CIs for paired t-test... I don't know the software used (none mentioned), and I don't have their raw data. All I know is that most of their CIs are ridiculous compared to my CIs calculated from their mean errors and SDs.
– Vic
Apr 25, 2014 at 13:31
• Which paper? It's possible you've missed some detail that changes things (e.g. a transformation). It's very difficult to make sensible comments with no context. Apr 25, 2014 at 13:32