BIASED SAMPLING; THE NONCENTRAL HYPERGEOMETRIC PROBABILITY DISTRIBUTION
Kenneth T. Wallenius · 1963
Consider a set S of L elements which is dichotomized in some manner (say, by an observable characteristic) into subsets M and N containing m and n = L - m elements, respectively, and a sampling mechanism which in some way selects a subset R of r elements from S. Let a be a realization of the random variable A denoting the number of elements in R arc of circle M. The hypothesis that the sampling mechanism is random is tested against the alternative of "non-randomness."