Development and Introduction of a Novel Method for Measuring Spatial Balance

Abstract

Spatial balance of samples in the space of auxiliary variables—especially when these variables are correlated with the target variables—plays a crucial role in improving accuracy and reducing the variance of statistical estimates. A uniform and dispersed distribution of sample units in this space, without the need to collect additional information, can provide a better representation of the population structure, since auxiliary data are usually already available. In recent years, various methods have been introduced for designing spatially balanced sampling, including the cube method, local pivotal sampling, and distance- or spatial correlation-based designs. The common feature of these methods is achieving samples with a balanced distribution in the auxiliary space. This paper develops and introduces a novel index for assessing the degree of spatial balance of samples. The proposed index is based on the Voronoi structure and provides a quantitative measure for evaluating spatial balance by analyzing the spatial relationships of each sample unit with its neighbors. Empirical results indicate that using this index can be effective in comparing and optimizing sampling designs and ultimately in reducing the variance of estimates.