We consider secret key agreement by multiple parties observing correlated data and communicating interactively over an insecure channel. Our main contribution is a single-shot upper bound on the length of the secret keys that can be generated, without making any assumptions on the distribution of the underlying data. Heuristically, we bound the secret key length in terms of "how far" is the joint distribution of the initial observations from a distribution that renders the observations independent across some partition of the set of parties. The closeness of the two distributions is measured in terms of the exponent of the error of type II for a binary hypothesis testing problem, thus bringing out a structural connection between secret key agreement and binary hypothesis testing.