SAMPLES OF TWO UNITS DRAWN WITH UNEQUAL PROBABILITIES WITHOUT REPLACEMENT1
- 1 November 1962
- journal article
- Published by Wiley in Australian Journal of Statistics
- Vol. 4 (3) , 89-100
- https://doi.org/10.1111/j.1467-842x.1962.tb00326.x
Abstract
The method of sampling without replacement suggested by Narain, with total probability of selection proportional to size, is considered in detail. The conditions under which it is of practical value are discussed. Narain's equations for the selection probability function are examined and it is shown that they do not yield the correct solution in every case. A revised set of equations is given which is proved to yield a unique correct solution for every possible case. From this investigation, a fast iterative method of solution is derived. Prooi is offered that there is always a decrease in variance compared with sampling with replacement. A formula derived by Sen (1953) in a slightly different context is used to obtain a positive unbiased estimator of variance. Finally, the case is considered where one unit covers more than half the stratum size.Keywords
This publication has 2 references indexed in Scilit:
- Selection without Replacement from within Strata with Probability Proportional to SizeJournal of the Royal Statistical Society Series B: Statistical Methodology, 1953
- A Generalization of Sampling Without Replacement from a Finite UniverseJournal of the American Statistical Association, 1952