This is not an answer - but it's too big for a comment. Your writing is simply unreadable. It might be salvageable if you used good practices for scientific writing. Here are the specific complaints.
- Your question is not written in complete sentences. Remarks like this are meaningless:
Given performance in columns, what is a predictor for which?... Generalise for any number of exams between pre and final.
- You refer to things that don't exist, like "row ID" and "student number" when there is no row ID nor student number.
- You excessively use dependent clauses. I found this line the most unreadable of all:
So, for example—using the regular Fail (F) is < 50; Pass (P) is ≥50 & ≤75; Distinction (D) is >75 & ≤ 85; and High Distinction (HD) is >85—show which exam—and quartile—predicts a more favourable final exam outcome?
- You don't define terms, then seem to use different terms equivalently, "marks", "columns", "outcome", "categorical variables", "quartiles" all seem to refer to one or more exam marks.
- You use shorthand and lazy typing when you need to specific. Here, what other "corresponding probabilities" might you be talking about. And what else could &etc. possibly mean?
&etc., with corresponding probabilities (incl. p values).
- Your writing is full of unnecessary adverbs:
Given the following dataset... I'm essentially trying to figure out...What test can I use for numerically explaining.."
As a tip: when people are confused on a subject, they tend to explain "wide" when they need to explain "deep". If you use consistent terminology, follow a structured format (like data - task - problem), and permit yourself only one question mark, the writing could be improved significantly.