ABSTRACT
The use of the term 'random' has given rise to a certain amount of confusion in the literature, due to a looseness in distinguishing between random sampling and unrestricted random sampling. The latter means that each possible sample of n units from a population of N units has an equal chance of being selected, which in turn implies that every member of the population has an equal chance of selection into the sample. Moreover, unrestricted random sampling is conducted 'with replacement', that is the unit selected at each draw is replaced into the population before the next draw is made; thus a unit can appear more than once in the sample. 1 Most statistical theory relates to unrestricted random sampling. 1 There appears to be no standard terminology to distinguish between this type of sampling with and without replacement. We follow Kish (1965a) and use 'unrestricted random sampling' for the former and 'simple random sampling' for the latter. Among other approaches are those of Cochran (1963), who also uses 'simple random sampling' for sampling without replacement but suggests that 'unrestricted sampling' is just an alternative phrase for 'simple random sampling'; and of Yule and Kendall (1950), who use 'simple sampling' to mean sampling with replacement.
