The closest I could think of is “empirical”, which the dictionary defines as “derived from or guided by experience or experiment”. Is there a more precise term that means “of or pertaining to data”?
Edit: And is there a better way to look something like this up? If I want to find a adjective form of a certain noun, what kind of reference book would I use? Dictionaries and thesauruses don’t seem to cut it.
I don’t think there is a word that holds to your “theory” analogy very closely. Could you construct a sentence with the desired word (written as a blank) used in context?
Example: “Instead of relying on blind conjecture, we should perform a data-driven analysis.” Is there a less clunky term that can replace “data-driven”?
In this context, “evidential” might be what you are looking for if what you want to convey is that what is being suggested is supported by data as opposed to speculation.