Abstract
The study examines the determination of stratification points for two study variables within the framework of simple random sampling, particularly focusing on calculating the population mean using a closely associated variable. Utilizing a superpopulation model, the investigation seeks to derive minimal equations by minimizing aggregated variance with the assistance of the variables under scrutiny. In order to improve the accuracy of estimating population parameters within a stratified sampling framework, it is suggested in the article to establish optimal strata boundaries (OSB) instead of categorizing variables, the study focuses on continuous variables for analysis. The creation of homogeneous units within each stratum, facilitated by optimally constructed OSB, leads to more effective sample sizes (SS) and consequently enhances precision in estimation. However, it's noted that the OSB and SS may not remain optimal in cases where a fixed total sample size is mandated, particularly in survey designs constrained by a fixed budget. To address this challenge, the article outlines a methodology for calculating the OSB and SS under the condition that the survey's per-unit stratum measurement costs or its probability density function is understood. An empirical demonstration of a design-based stratification approach is showcased using breast cancer data, where the mean perimeter is estimated based on mean radius and mean texture. Furthermore, numerical examples are provided for hypothetical study variables following Cauchy and standard power distributions. The novel approach has been integrated into the revised stratifyR package and LINGO software. The research outcomes indicate that the newly introduced method demonstrates superior efficiency or comparable performance when aiming to refine the precision of population parameter estimations.