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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.

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to my knowledge, there is no "default" way for comparing two distributions. It always depends on what you're looking for. Here are few simple suggestions.

If I understand your problem correctly, normalizing your distributions will not be helpful - at least if the range/deviation of the values is an "information" in your data (see no. 1 below).

  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.

  3. You may compute the difference of the distributions and integrate (summarize) the differences' absolute values. This also requires histogram-like data, so similar signals are counted in the same categories.

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