The most natural phrasing for similar contexts would be...
Here are the test scores grouped by [student nationality, or whatever].
...but OP's categorisation system already includes the word "group", so to avoid sounding clumsy he should simply omit the word before "by"...
Here are the test scores by student group.
Note that "grouped" is always optional in such constructions, but it's usually better included.
Taking the pedantic line, grouped by may be more appropriate if individual student test results are presented in a list containing a separate section for each group, and plain by if the only values shown are totals/averages for each group.