# Test for difference between 2 empirical discrete distributions

I have test data where I have several large samples from discrete distributions which I am using as empirical distributions. I am wanting to test whether the distributions are actually different and what the difference in means is for those distributions which are actually different.

Since they are discrete distributions my understanding is that the Kolmogorov-Smirnov test is invalid due to the underlying continuous distribution assumption. Would the Chi-Squared test be the correct test for whether the distributions are actually different?

What test would I use for the difference in means? Would a better approach be to sample from the distributions and take the difference and then perform analysis on the distribution of the difference?

• Yes, the $\chi^2$-test is the correct one. The accepted answer to this question elaborates on that. distribution 1 = urn 1 and distribution 2 = urn 2. There, the values of the random variables are colours and in your case probably something else, e.g. discrete numbers. – Georg Schnabel Mar 4 '14 at 19:36
• Thank you for the feedback. Is there a test for what the difference in means for when the chi-squared test confirms that the distributions are different? – Wallhood Mar 4 '14 at 19:53
• Would a better approach be to sample from the distributions and take the difference and then perform analysis on the difference? – Wallhood Mar 4 '14 at 19:59