Assessing the Effect of Sampling Frame Design on Population Representation and Statistical Estimation Precision

Posted: Feb 05, 2023

• Jordan Morris
• Joseph Kelly
• Julia Foster

Abstract

Sampling methodology represents a cornerstone of statistical practice, enabling inference about populations through examination of subsets. While extensive literature exists on sampling techniques, selection methods, and estimation procedures, the fundamental construction of sampling frames has received comparatively limited systematic investigation. The sampling frame serves as the operational representation of the target population, yet its construction is often treated as a practical concern rather than a theoretical component of the inferential process. This research addresses this critical gap by examining how sampling frame design fundamentally shapes both population representation and statistical estimation precision. Traditional sampling theory typically assumes the existence of a complete, accurate frame from which samples are drawn. In practice, however, frames suffer from various imperfections including undercoverage, overcoverage, duplication, and temporal misalignment with the target population. These imperfections introduce systematic biases that propagate through subsequent statistical analyses. Current methodological approaches tend to focus on post-hoc adjustments through weighting or modeling, rather than addressing frame quality at its source. This research proposes a paradigm shift by establishing frame construction as a primary determinant of inference quality. Our investigation centers on three innovative frame construction methodologies that address common practical challenges. Adaptive mesh refinement addresses heterogeneous population structures by dynamically adjusting frame resolution based on population density and variability. Temporal synchronization techniques align frame construction with population dynamics, particularly relevant in contexts of high mobility or rapid change. Multi-source fusion integrates incomplete administrative sources to construct more comprehensive frames than any single source could provide. Through rigorous simulation and empirical validation, we demonstrate that these approaches substantially improve both representation accuracy and estimation precision compared to conventional methods.