CONSTRUCTION OF STRATA FOR A MODEL-BASED ALLOCATION IN STRATIFIED SAMPLING FOR TWO STUDY VARIABLES

This paper proposes a few methods of stratification for two study variables, contributing to the extensive body of research on optimum stratification in stratified sampling, for a known model-based allocation. The methods of finding points that stratify a heterogeneous population optimally have been obtained in the form of equations. These equations, which yield the optimal points for stratification (OPS), for the model-based allocation, are derived by minimizing the determinant of the variance-covariance matrix of stratified sampling for two study variables. However, these equations are lengthy as well as implicit, making them difficult and cumbersome for practical implementation. Therefore, the equations are algebraically and analytically transformed to derive a few methods for obtaining approximately optimal points for stratification (AOPS). The efficiencies of all the proposed methods are empirically evaluated using a few generated populations with results showing consistently efficient performance in stratifying populations optimally. The equations yielding OPS and their transformed methods yielding AOPS have demonstrated similar efficiencies in their performance. This suggests that the simpler and easy-to-use AOPS methods can serve as effective substitutes for the implicit and lengthy equations. All the methods proposed herein are derived under simple random sampling with replacement (SRSWR) design, but they are found true in simple random sampling without replacement (SRSWOR) provided finite population correction is neglected.