I'd like to have your thoughts on the following problem. I want to study the relationship between two quantitative variables X and Y, one of them, say X, having lots of zeros (e.g. 30% or 50%). I decide to divide the variable X in 3 classes, one class being made of zeros. Then Kruskal-Wallis test tells me variable Y is not different between the 3 X classes. But I see on a boxplot of Y conditional on X that Y seems to have a similar distribution in two contiguous X classes but to have much smaller values in the third class. Do you think it is statistically correct to perform a Mann-Whitney test (that is Kruskal-Wallis test applied to the case of comparing only 2 groups) to compare the distribution of Y after having gathered together the two X classes where Y behaves similarly? It doesn't seem fair to me but I can't clearly explain the potential problem.
Thank you in advances for your ideas.
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