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On Relative Precision in Stratified Sampling for a Mean with Fixed Cost
Author(s) -
Bennett B. M.,
Islam M. A.
Publication year - 1986
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710280815
Subject(s) - mathematics , upper and lower bounds , statistics , sampling (signal processing) , sample size determination , combinatorics , population , variance (accounting) , zero (linguistics) , stratified sampling , mathematical analysis , physics , linguistics , demography , accounting , philosophy , detector , sociology , optics , business
This paper considers the extrema of the relative precision (R. P.), or the ratio of the variance of optimum allocation to that of proportional allocation in stratified sampling for a mean (= Y ) or total (= Y ) when there is a fixed cost C = c o +σ n h c h over L strata. The upper bound of R. P. is shown to be equal to unity, though the lower bound can be negative while approaching zero if the finite population size N →∞. Numerical results (cf. Table) when the upper bound of R. P. = 1 is attained are included for the cases L ≦4 with various combinations of { W h }, { c h } and a fixed cost C ; these give the appropriate sample sizes (= n p ) determined for proportional sampling in the cases of finite populations of sizes N =5000, 10,000 respectively.