There is insufficient context for us to advise you. What is the relationship between the two groups and the PET test? In any case you need to insert an article (a or the) before 'PET'. Which you insert will depend on the overall meaning. Could you please give us more context?
It is related to statistics. I have two groups (two independent variable) and I want to compare the results of these two groups using a PET test.( a kind of proficiency level test). PET by groups.
I just want to know if I should use preposition on after compare or not.
"We compare the two groups on/in/about a PET test."
I am not a statistician so I hope you will get expert advice on this from another Forum member. Personally, in my ignorance, I would suggest "by means of a PET test". None of your three alternatives would mean anything to me as a lay reader.