# help interpreting t-test and p-value - or help me finding a good statistical test

I have two samples

background

and

input

these are the histograms:

sample sizes are well above the 1000s, so the sample variance of the mean is pretty much low.

I'm trying to have a statistic that tells me that these two distributions are the same. I'm trying with t-test and Mann-whitney U but both have VERY low pvalues (10^-100 and lower).

I understand that this is because the sample sizes are large and the sample mean can be considered separated even if very near (because of very small sample variance), but here lies the core of my problem.

I don't have a background in statistics (physics major) so forgive me if I use wrong terms, correct me please.

• "I'm trying to have a statistic that tells me that these two distributions are the same." .... no statistic can tell you they're the same. At best you can see if they're not inconsistent with having come from the same distribution (which is not at all the same thing). Even if the samples were identical it doesn't mean they were necessarily drawn from the same distribution. Commented Mar 21, 2017 at 0:11