Political Districts Versus Customized Polygons: Implementing Geographic Tessellation Stratified Random Sampling

ABSTRACT This paper explores the intricacies of spatial probability sampling designs, with a specific focus on the neglected topic of comparing artificial areal unit support networks with the convenience of existing political districts, and the role of spatial autocorrelation (SA) in this interplay. The traditional approach when controlling for variable probability selection in spatial sampling often involves creating customized areal units, such as regular hexagons forming a tessellation. However, this method introduces operational challenges, requiring significant upper‐level government coordination and oversight due to their lack of hierarchical nesting within existing administrative units. The primary aim of this paper is to better understand the role of spatial autocorrelation as well as evaluate the advantages (e.g., convenience) and weaknesses of transitioning from ideal equal‐area regular polygons to irregular surface partitionings based on political boundaries for geographic tessellation stratified random sampling (TSRS) designs. The analysis expands on previous work by considering a wider range of empirical geographic landscapes and attribute variables, including real‐world spectral indices derived from remotely sensed data. Including attributes with positive SA and noise levels introduces a more realistic assessment than achieved in earlier studies that relied upon smoothing data‐generating processes. Implications and conclusions drawn from this research underscore the complex trade‐offs in choosing between artificial areal units and existing political districts for TSRS designs. Although TSRS offers benefits such as improved geographic landscape coverage, cost‐effectiveness, and ease of implementation within established administrative frameworks, it does not guarantee enhanced statistical precision compared to simpler sampling methods. Ultimately, this paper presents compelling evidence that utilizing political districts for TSRS may often be preferable—re convenience and the role of SA—to customized artificial polygons—whose forte is controlling for variable probability selection while attempting to effectively handle SA—especially considering practicality and overall inferential diversity affiliated with spatial sampling.