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I have a data set of 1 categorical predictor (4 levels) and one non-negative continuous response variable (listed as "aphidleaf in histogram). The response variable is not count data and the zeros are important. I am interested in comparing the means of the groups, and was planning a one-way ANOVA until I looked at the data.

My response variable is highly zero inflated (see frequency histogram). I have tried many transformations and have decided to use a nonparametric test. Kruskal Wallis will be straightforward and appropriate for my question to determine any difference in response variable between the treatment groups, but I found that there is a zero-inflated Kruskal Wallis test. Does anyone have any experience with the difference between the two or any to choosing one over the other? https://github.com/chvlyl/ZIR

I know Kruskal Wallis is familiar to many people, so I wonder if it is a more widely accepted approach than the zero-inflatedzero-inflated histogram

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  • $\begingroup$ Try the ZI Kruskal Wallis test. paper by Wang, Chen and Li (2021) available on MathArch. the titke is "Rank-Based Tests for Nonnegative Data with Excessive Zeros with Applications to Microbiome Data". R code available, works well. Good luck SH $\endgroup$
    – steph
    Oct 26, 2022 at 3:18

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The solution needn’t be very complicated. Rank tests can handle extreme numbers of tied values if you are a bit careful in computing p-values. It is best to use the generalization of the K-W test, which is the proportional odds ordinal logistic semiparametric regression model. The PO model can handle extreme ties, since it reduces to the binary logistic model if there are only 2 distinct Y values. See here for resources.

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  • $\begingroup$ If you run the PO regression on the four-level factor variable, however, then isn’t chunk testing the coefficients equivalent to KW? Even if zero-inflated KW can’t be generalized to a full regression setting like regular KW can, I wonder how the two compare when we are in a simple setting. $\endgroup$
    – Dave
    Dec 17, 2023 at 13:04
  • $\begingroup$ Yes except P-values from likelihood ratio tests using the PO model may be more accurate when there are many ties. The real question is whether you need to explicitly handle zero inflation. I doubt it. If you do, then a Heckman 2-stage model may be worth a look (model Pr(Y=0) then Pr(Y | Y>0) and put them together). $\endgroup$ Dec 17, 2023 at 13:37

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