AbstractBanked set sampling theory introduced by Mclntyre (1952) is generalized by introducing a Selective Probability Matrix. The theory is intended to make full use of available information and is most useful in situations ‐where a random sample of small size can be readily ordered by visual inspection or other rough gauging methods, and the exact measurement of the sample is costly in time or effort.In this paper an estimator of the population mean is constructed and several properties of it are investigated to demonstrate the advantages of the theory. The cases of perfect ranking and errors in ranking are discussed in detail and it is made clear that errors in ranking do not destroy the usefulness of the metho