In trying to determine whether a disease is familial, epidemiologists often locate a source of cases and compare the proportion of affected relatives of these cases with that of the relatives of controls by the usual fourfold table techniques. In the model considered here, following Haenszel [5], the probability of being affected is a random variable, ρ, which is constant for members of the same “family” but which may vary from family to family. The usual tests are examined under a sampling scheme designed to simulate actual epidemiological practice, and it is found that if ρ is the same for all families, the proportions of affected relatives in the two groups are distributed as binomial proportions from the same universe. If ρ is not constant, the proportions are no longer binomial, but the tests used are shown to be consistent nevertheless. A large sample confidence interval forEρ is derived.