Apologies if this is a really simple question; I'm sure if only I knew what to google I'd be able to find the answer myself, but it's been driving me mad.
I have two datasets with approximately gaussian distributions. Both are measurements of the same background distribution, taken for reproducibility of some optical instrumentation I've developed. I need to prove this using the two measurements.
My understanding is that to achieve this, I integrate common area that's underneath both measured distributions. However...
In my case, gaussian 1 has a mean of 41.3 and a standard deviation of 1.0. Gaussian 2 has a mean of 41.7 and a standard deviation of 1.6. This means that the two gaussians intersect twice.
When I integrate the common area, I get 0.76, which I interpret to mean there's a 0.76 probability that the two measurements are of the same background distribution. This sounds way too low to me.
I had a look at KL divergence, but this is asymmetric and assumes that one of the measured distributions is the 'true' distribution - this is not the case for my measurements.
I have some more similar comparisons with more than two measured distributions to worry about, but I'd like to walk before trying to run...