IMPROVING VARIANCE PRECISION IN POPULATION STUDIES: THE ROLE OF POST-STRATIFICATION AND AUXILIARY DATA

In this study, we propose an enhanced estimator for the finite population variance in the context of post-stratified sampling, incorporating an auxiliary variable to improve accuracy. We derive expressions for the bias and mean square error (MSE) of the proposed estimator, providing an approximation accurate up to the first order. The theoretical analysis highlights the conditions under which the proposed estimator yields lower bias and reduced MSE, making it a more efficient alternative to traditional methods. To evaluate the practical performance of this estimator, we apply it to two real-world data sets, where our results demonstrate a marked improvement in efficiency over existing estimators. The numerical findings confirm that, in post-stratified sampling, the proposed estimator significantly enhances the precision of variance estimation, especially when the auxiliary variable is highly correlated with the study variable. This work not only contributes a more efficient estimator but also provides valuable insights into the application of auxiliary information in post-stratified sampling designs.