# Compare two samples with many zeros

We carried out a number of some experiments and got 10 independent 2-samples datasets.

Is it possible to show a significant difference between the two samples, if each of them contains more than 75% zeros (and we don't want to exclude zeros from these samples)?

Example of sample's box plots obtained by one of our experiments below:

It is important to note that in 10 independent models (experiments) the difference is approximately the same visually, but Kolmogorov-Smirnov, Brunner-Munzel and Wilcoxon tests show unstable p-values for different models.

What statistical test should we use to show the significance of differences in these cases? Or zero-values filtering is necessary?

• What do you refer to with "significant difference between the two samples"? Significantly different mean? Or do you want to a more general check testing if both samples come from the same distribution? – David Mar 26 at 12:39

I think the supremum should be quite different even when we include 0s and hence K-S stat should be significant. Can you please elaborate, what you mean when you say $$p$$ values are unstable? Do you mean, they differ vastly across the 10 experiments? Can you share empirical cdf plots?