# How to compare two groups of empirical distributions?

I am working with EEG and now I am trying to compare coherence for two groups of individuals. Problem is coherence is dependent on length of signal but I have signals with different length for each individual. So I decided to divide my signals on equal pieces and randomly choose fixed number of pieces for each individual. It's working fine, but I'm not happy about loss of data. Then I realised that I can repeat this choosing fixed number of pieces and calculating coherence many times for each individual. It gives me empirical distribution of coherence for each individual. So my qvestion is: How to compare two groups of empirical distributions where each distribution come from one individual?

I found related question. Is this method appropriate in my case? I tried to normalize my data as in accepted answer on this question with log, arctan, sqrt transform. But with no success.

1. If the data is (nearly) normally distributed or can be transformed into something nearly-normally distributed (log, logit, etc.), you may simply compute the mean and sd for each distribution and compare those.
2. You may create histogram-like data (i.e., count the distribution in few categories) and compute a simple correlation between the two sets.