I am currently coming towards the end of my dissertation, and I am looking for a bit of help with how to test distributions using a chi squared test with the data that I have. I have attached a picture of mocked up data that represent what I am trying to test.

The first table is a raw set of occurrences for each subject split out across a number of different criteria. The second table shows proportions of an occurrence in each criteria (so what % of occurrences happen within each criteria). Note they are disjoint and independent, so sum to 1.

In addition, I have grouped my subjects into two groups, (A and B). Essentially, I want to test if the distribution of observations is significantly different across the different criteria for my two groups.

I know I have (at least) two ways I could proceed:

1) Sum the values across the various groups to get a total number of occurrences in each criteria by group.

2) Sum the values like in 1), but then calculate overall proportions for each criteria, for my two groups (so kind of like a mean proportion for each criteria for each group).

In order for the test to be valid, I believe I need to proceed similar to option 2). Are there any violations of assumptions I need to be aware of in this case? Otherwise, is this a valid way to proceed? Or is there a better approach I could use?

Many thanks in advance,

Tom