# testing dependent skewed samples

I must compare two distributions of patent data: namely, they are the number of patent applications of companies before vs after an acquisition. I need to perform an hypothesis test to assess if the change in the number is significant.

The data are dependent (number before and number after) and extremely skewed (a lot of zeros and a few higher values).

It is clear that I cannot use the t-test and surfing the internet I was not able to find a test for both not normal (strongly skewed) and dependent samples.

I was thinking about the Wilcoxon Signed-Ranks Test for Paired Samples (http://www.real-statistics.com/non-parametric-tests/wilcoxon-signed-ranks-test/) but it seems the distribution should not be very skewed. May I use it anyway? If not, which one should I use then?

EDIT: I found an answer here (Appropriateness of Wilcoxon signed rank test). I understand that skeweness is not a big issue for the Wilcoxon test, so I will use that one. However, if somebody does not agree or has some comment I would be glad to hear them. Thanks.

• Is it possible for the number of patents to go down? Does this really need to be tested? Dec 14, 2015 at 12:03
• You are right I did not explain correctly: it is actually the number of patent applications. Dec 14, 2015 at 12:19
• Samples are neither parametric nor nonparametric; they're adjectives that apply to models or techniques. If you mean "not normally distributed" that's not at all the same thing as "nonparametric" and similarly "parametric" is not at all the same thing as "normally distributed" -- one can fit parametric non-normal models and correspondingly, one can quite reasonably use nonparametric procedures on data drawn from normal distributions. Dec 14, 2015 at 13:36
• thanks for the correction :) I will update my question accordingly. In my case, I meant I have a not normal distribution. Dec 14, 2015 at 13:58