Kruskal-Walis interpretation with too many outliers and "0" values I want to establish significant differences between certain groups. I have a dependent variable that is named "NRPS BGCs" which are the presence of certain genes founded in certain bacterial species.
Here there are some descriptive statistics of my data:

Here is a box plot:

I tried the Shapiro test for normal distribution tendency of my data, and it resulted in a non-normal distributed data, so I think that the Kruskal-Walis test is the appropriate statistic to apply, but not pretty sure of that given the fact that the median values along the different groups are 0s and 1s.
I have a lot of outliers on this data as it is seen on the box plot, these outliers provide relevant biological information of gene expression, so how can I handle these outliers ahead to make a correct interpretation of Kruskal-Walis?
Using Kruskal-Walis test I got a p-value <0.001 so I can reject the null hypothesis, and establish that there are significant differences between groups but not sure if I can trust on this given the outliers.
Is it okay to get into that conclusion having so many outliers?
 A: The null hypothesis of a Kruskal-Wallis test extends the null hypothesis of a rank sum test from comparing $k=2$ groups to comparing $k\ge 2$ groups, so becomes:
$$\text{H}_{0}\text{: }P(X_{i} > X_{j}) = 0.5\text{ with }\text{H}_{\text{A}}\text{: }P(X_{i} > X_{j}) \ne 0.5\text{, for }i, j \in 1, 2, \dots k,\text{ and }i \ne j$$
This is a null hypothesis that a randomly observed value from any group $i$ is neither more nor less likely to be larger than a randomly observed value from any (other) group $j$. Rejecting the Kruskal-Wallis null hypothesis means that you found evidence that in at least one group a randomly observed value is more likely to be larger than a randomly observed value from at least one other group.
Being a rank-based nonparametric test, the Kruskal-Wallis is insensitive to outliers (in the way that we typically think of sample means and variances as being sensitive to outliers), and generally relies only on observations within each group having identically distributed values with finite (and existing) means and variances.
If all groups have (i) the same shape distribution, and (ii) the same variance, then you can interpret the Kruskal-Wallis null as an omnibus of 'equal means' or 'equal variances' with the alternative hypothesis being 'at least one group mean differs from at least one other group mean' or 'at least one group median differs from at least one other group median.' However, these are strict assumptions, and your box plots appear to illustrate violations of both (e.g., Myxococcota looks to have a possibly symmetric distribution, contrasting sharply with the 0-weighted distributions of many other groups, the variances appear to quite different, etc.). Therefore, your interpretation should be limited to "There is evidence that least one group is 'stochastically larger' than at least one other group at the $\alpha$ level of significance."
