# Help with confidence intervals

I am trying to understand confidence intervals better.

If two different labs ran the same experiment, with the same number of samples and both got the same mean values but their 95% CI differed.

Lab 1 got a mean value of 1.6 & 95% CI: 1.0 to 2.2

Lab 2 got a mean value of 1.6 & 95% CI: 1.5 to 1.7

What could you actually deduce from this?

If you took both results separately, would you be any more confident that the true mean was 1.6 from the results from lab 2? I feel like I am not really understanding what a CI is and misinterpreting it.

• @mkt I suspect you intended to write the opposite of some of the things you did. First, it is clear that the variance was much smaller in the Lab 2 sample than in the Lab 1 sample. Second, your reference to "probability density" sounds like you are taking these to be Bayesian credible intervals rather than confidence intervals, because it isn't clear to what "probability density" actually refers. As such, your comment might confuse the issue more than clarify it.
– whuber
Commented Jul 17, 2017 at 13:53
• This is a problematic question because although you can deduce something about the mean by combining these CIs, something else unrelated to CIs is going on. Because one interval is so much narrower than the other, you have produced significant evidence that the variances observed by the labs differ. That would make one hesitate to interpret the CIs (or to combine them) until the reason for this difference in variances is better understood.
– whuber
Commented Jul 17, 2017 at 14:11
• As whuber said, in your case it means that there is a significant difference in variance between the samples. A rule of the thumb is that, when the C.I. of the samples do not overlap, then there is a significant difference between the sample statistics (not your case). Another one is that, when a C.I. contains 0 in its range (i.e. one of the intervals is negative), then you simply don't have good enough data to estimate an interval at that confidence level. Commented Jul 17, 2017 at 14:27
• @whuber Fair points, that was sloppy writing. I am deleting my previous comment.
– mkt
Commented Jul 17, 2017 at 14:48
• @Digio Please be careful, lest you confuse readers even more. Although it's correct that non-overlap of CIs often implies significance, the inverse is not true. See stats.stackexchange.com/questions/18215. Moreover, a CI has nothing whatsoever to do with containing zeros or not: you must be thinking of using a CI in a particular kind of null hypothesis test, one that is not germane to this discussion. Your characterization of a CI is disputed by almost everyone; in particular, (1) is misleading and (2) is strikingly false.
– whuber
Commented Jul 17, 2017 at 17:35