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Zero-inflated data

I have zero-inflated (~90% zeros) data which is distributed like the left-hand figure above (the right-hand figure shows how when log-transformed, the non-zero component of the distribution is approximately normal). My null hypothesis is that there is no significant difference between two sets of data which are distributed as above.

I want to know if there is an appropriate non-parametric statistical test which will tell me whether there is a significant difference between two such distributions. Preferably I would like to be able to tell whether some measure of centrality or other of one dataset is significantly higher than that of the other.

The best I can do so far is the Wilcoxon signed rank test (the data is paired), which I believe is telling me that one distribution is significantly different from another. I am unsure however, whether is appropriately addresses my hypothesis.

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    $\begingroup$ I'd be inclined to think about whether a permutation test might be suitable. On the other hand, I'd also be tempted to consider a parametric approach based on a zero-inflated distribution. $\endgroup$
    – Glen_b
    Aug 27, 2015 at 13:03
  • $\begingroup$ How might one apply a permutation test in this case? $\endgroup$
    – niafall
    Aug 27, 2015 at 13:16

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You should use the Mann-Whitney U-test if the samples are not paired. The Wilcoxon signed rank test is for paired data. I don't think that the number of zeros matter in this case.

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  • $\begingroup$ Ah, apologies. The samples are paired, I will amend the original post accordingly. When one applies the Wilcoxon signed rank test, is the null hypothesis that there is no difference between the distributions? Is the statement of the hypothesis relating to some statistic of the distribution or just the overall dataset? $\endgroup$
    – niafall
    Aug 27, 2015 at 12:14
  • $\begingroup$ I think that the null hypothesis is that the mean ranks does not differ between the groups. It does relate to the W statistic. It is explained very well in this wikipedia article: en.wikipedia.org/wiki/Wilcoxon_signed-rank_test $\endgroup$
    – JonB
    Aug 28, 2015 at 13:05

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