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OPTIMUM STRATIFICATION FOR TWO STUDY VARIABLES FOR ALLOCATION PROPORTIONAL TO AUXILIARY VARIABLE STRATUM TOTAL
Keywords:
auxiliary variable, study variable, optimum points of stratification, superpopulation model, stratified simple random sampling with and without replacement.DOI:
https://doi.org/10.17654/0972361722087Abstract
In this paper, we consider the problem of optimum stratification for two study variables based on an auxiliary variable which is highly correlated with the study variables for allocation proportional to stratum total of the auxiliary variable. Equations giving the optimum points of stratification (OPS) have been derived by minimizing the determinant of the variance-covariance matrix of the study variables. Because of their implicit nature, the equations giving OPS are trivial to solve and, therefore, a few methods of finding approximately optimum points of stratification (AOPS) have also been obtained as the solutions to the equations giving OPS. The efficiencies of the proposed methods of stratification are examined empirically in a few generated populations and found to be highly efficient. The methods proposed herein are obtained under simple random sampling with replacement (SRSWR) design which holds true for simple random sampling without replacement (SRSWOR) too when the finite population correction is neglected.
Received: September 28, 2022
Accepted: November 15, 2022
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