# quantify difference between discrete distributions

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John on 14 Feb 2013
Hello,
I am trying to quantify the difference between two discrete distributions. I have been reading online and there seems to be a few different ways such as a Kolmogorov-Smirnov test and a chi squared test.
My first question is which of these is the correct method for comparing the distributions below?
The distributions are discrete distributions with 24 bins.
My second question is that, it pretty obvious looking at the distributions that they will be statistically significantly different, but is there a method to quantify how different they are? I'm not sure, but a percentage or distance perhaps?
I appreciate any help and comments
Kind Regards

Thorsten on 14 Feb 2013
Use the Two-sample Kolmogorov-Smirnov test from the Statistics Toolbox.
John on 16 Feb 2013
Edited: John on 16 Feb 2013
In the example in the documentation, doc kstest2, p is less than k and the hypothesis is not rejected. You say "could not be rejected if p >= k"
In your previous post you said "A measure of how different they are will be the p-value", but in my case P is very small??
José-Luis on 16 Feb 2013
Edited: José-Luis on 16 Feb 2013
The smaller p , the larger the difference between distributions. It's consistent with what I said before, methinks. It is a comparative measure, and you need to know what you are comparing against (in this case k). How to define k is a different story, for that you need to read the paper of those who came up with the statistic.
Also, you should be careful how you phrase the results from an hypothesis test. In this case, I should have said: "if _p>=k then the hypothesis that both samples come from the same distribution cannot be rejected".