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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?

Thanks in advance.

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.

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  • $\begingroup$ Is it possible for the number of patents to go down? Does this really need to be tested? $\endgroup$
    – gung - Reinstate Monica
    Commented Dec 14, 2015 at 12:03
  • $\begingroup$ You are right I did not explain correctly: it is actually the number of patent applications. $\endgroup$
    – jimmy
    Commented Dec 14, 2015 at 12:19
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    $\begingroup$ 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. $\endgroup$
    – Glen_b
    Commented Dec 14, 2015 at 13:36
  • $\begingroup$ thanks for the correction :) I will update my question accordingly. In my case, I meant I have a not normal distribution. $\endgroup$
    – jimmy
    Commented Dec 14, 2015 at 13:58

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You could use a nonlinear multilevel model where the dependent variable is number of patents and the IV is time (before or after). Then you could choose a zero inflated negative binomial for your function.

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  • $\begingroup$ I think this may be is a little beyond my statistical skills! I was looking for something that I could run on Excel. I admit maybe it is not possible. $\endgroup$
    – jimmy
    Commented Dec 14, 2015 at 12:23
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    $\begingroup$ I would not use Excel for statistics. You may need to hire someone to do this for you. $\endgroup$
    – Peter Flom
    Commented Dec 14, 2015 at 12:53
  • $\begingroup$ What is the reason for a multilevel model in this case? What about analyzing the differences after-before, and bootstrap that? $\endgroup$
    – kjetil b halvorsen ♦
    Commented Dec 14, 2015 at 13:50
  • $\begingroup$ @kjetilbhalvorsen that's another possibility but I think it can wind up correlating errors. However, with this data there may be very little error. $\endgroup$
    – Peter Flom
    Commented Dec 15, 2015 at 12:02

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