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I want to test for a trend in a continuous (non-normal) response variable across ordinal categories.

I came across multiple test that seem suitable for this problem. Particularly, the R package PMCMRplus contains a whole set of trend tests (Cuzick, Johnson-Mehrotra, Jonckheere-Terpstra, Le, Spearman, Murakami’s BWS, Chacko).

I wonder what are the differences between those tests? Is it possible to give recommendations when to use which one?

So far, I figured out that Johnson-Mehrotra is meant for balanced groups, i.e. equal group size for all categories. What are the properties, assumptions, requirements of those different tests?

If you can elaborate on individual tests, that would be much appreciated. Even more so, if you could compare different tests to each other.

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