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I have a distribution of discrete values (grades, from low to high) where I see that the certain groups have a higher frequency of observations in the higher ranges and less in the lower ranges than other groups. Eyeballing the histogram they are thus performing better.

I would like to see if these differences in the different groups are significant. e.g. is it true that group B has significantly less (more) low (high) grades compared to group A.

Is it best if I decompose the data between the different ranges (high/low)? Or are there other techniques that could be useful?

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  • $\begingroup$ Have you tried Mann-Whitney or (for several groups) Kruskal-Wallis? $\endgroup$ Commented May 2, 2022 at 10:47

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I believe what you are looking for here is what is commonly referred to as an ordinal regression. This term is used in my field to refer to a few different types of models that are used when the response variable is a set of ordered categories like you have with grades.

Here is a tutorial on fitting these types of models with a well-known R package expressly made for this type of regression: https://cran.r-project.org/web/packages/ordinal/vignettes/clmm2_tutorial.pdf

Here is a published paper going over explanations of these types of models: https://journals.sagepub.com/doi/full/10.1177/2515245918823199

I hope this helps!

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