What statistics can compare individual survey responses & others that were measured as a group (from which we need to extract individual responses)?
Sounds like you're looking for a hierarchical model. You might find some joy in  BDA, http://www.stat.columbia.edu/~gelman/book/ (in particular, chapter 5)

To quickly get some idea if this sort of thing is right for you, you could check out this blog-post on one particular example here http://andrewgelman.com/2014/01/21/everything-need-know-bayesian-statistics-learned-eight-schools/

Whether this will work for you also depends quite a bit on what you want to ask (what does 'identify the relationship' mean?) and the target audience. If you do head over to Cross Validated (strongly recommended!) make those things as clear as possible in your question.