Constructing efficient strata boundaries in stratified sampling using survey cost

Abstract

For maximum precision in population parameter estimation under the Stratified sampling design, the optimum strata boundaries (OSB) could be constructed based on a continuous study variable rather than a set of categorical variables. If constructed optimally, the OSB results in homogenous units within each stratum leading to optimal stratum sample sizes (OSS) as well. The OSB and OSS may not remain optimum if the problem is considered in terms of a fixed total sample size, especially when a survey design involves a fixed budget. This article suggests a methodology for computing the OSB and OSS when the per unit stratum measurement costs for the survey or its probability density function are known. To plan for such a stratified survey, we demonstrate a design-based stratification empirically by using Wave 18 of the HILDA Survey general release dataset where we estimate the mean level of Gamma-distributed annual total disposable income in Australia, which could potentially be an important variable for policy decision-making. We also provide numerical illustrations for hypothetical study variables that follow exponential and right-triangular distributions respectively. The findings indicate that the suggested method is satisfactory in the sense that it is either more efficient or relatively comparable with other methods aimed at improving the accuracy of population parameter estimates. The proposed technique has been implemented in the updated stratifyR package.

Keywords

• Optimum stratification
• Stratified random sampling
• Survey cost
• Sample allocation
• Dynamic programming