Where two confidence intervals meet? I have two means that refers to two different samples of different populations. Let's say, for example, that the two means are 1.0 and 3.15. I can compute confidence intervals about these two cases and, logically, higher is the confidence interval, larger are the two intervals (they tend to infinite width).
So, the question is: is there a way to find out the point in which these two confidence intervals meet?
 A: The exact answer depends on what are the intervals about and other circumstances but I'm going to made a couple of assumptions in the hope they fit your problem:


*

*You are computing confidence intervals on the mean.

*Your samples are large (let's say, at least over 100). If that assumption is false, then the answer here is just an approximation.


(For statisticians reading this, the second assumption means that for sake of simplicity I'm going to use normal distribution instead of t-Students and using standard deviation of sample).
You can compute means and standard deviation of both samples, and let's denote them mean1, mean2, sd1 and sd2.
Now you can use the following formula:
$$
z=\frac{(mean2-mean1)}{sd1+sd2}
$$
That $z$, in a normal standard distribution, is the one that contains between -z and +z the same probability of the level of confidence of your intervals when they start overlapping.
If you are interested in the point of overlapping, you just need to do:
$$
point=mean1+z*sd1
$$
or
$$
point=mean2-z*sd2
$$
and both should yield the same point.
If you need to know the confidence level of your intervals, you just need to check $z$ in a normal standard distribution table (like this one). If $p$ is the probability you get in the table you can find the confidence level by:
$$
CL=1-2*(1-p)
$$
If your samples are not large, and especially if they are small and of different sizes, the problem is a little different and it needs to be solved numerically - although an Excel spreadsheet can be enough to handle it. 
