you could just survey the source the kids are exposed to..
what is the vocabulary of "sesame street"? or Mr Rogers? compared to "scoobie doo"? how much time does the kid spend watching sesame street, how much time does the kid spend watching scoobie doo?

and just watch the parents.. invite them in for a paid study, tell them they might have to wait a few hours, but will have a place for kids to play and will get free lunch.
only the real study is the wait time.. how do they use it? do they talk and play with their kids? pick up available books and read? or do they generaly let the kids play by them selves, and not talk or interact with them?

if they kid picks up a truck, and says truck! does momma say Oh yes, a big yellow dump truck! (and teach big, yellow and dump?) or does momma say "Yes, a truck!" (a positive response, but not one that is vocabulary building-- remember these are basicly good mothers, good people)

at lunch does mommy say "eat your Tuna salad, you like tuna salad!"? (a positive statement) to define the sandwiches? or does she say "Yummy, tuna, with celery, and onions and pickles, with creamy mayonaise! Oh tuna salad is my favorite sandwich.." (a detailed, word rich response)?

no mother is perfect-- and many times my mother had a rich detailed vocabulary.. but sometimes "what's for dinner?" was answered with "food!"-- but in the course of three of four hours, you might see a big difference in quantity of words, and quality of vocabulary.

and if i can think of something like this, with very little background in sociology-- i bet there are even better ways.. and that the studies have been done.