How to find the best sampling design: A new measure of spatial balance

We present a novel measure to assess the spatial balance of a sample by utilizing the balancing equation, which captures the balance between the sample units and their neighbours. Spatially balanced samples are desirable as they may reduce the variance of an estimator of a population parameter. If the auxiliary variables we employ to spread the sample possess high explanatory power for the variable(s) of interest, the resulting reduction in variance can be substantial. An advantageous aspect of using auxiliary variables is that their availability is not contingent upon the sampling effort. Therefore, we can assess and compare sampling designs before committing resources to full-scale surveys. By comparing the proposed measure with commonly used measures of spatial balance, we ascertain that our measure consistently yields meaningful insights regarding the spatial balance of samples. Consequently, our measure can effectively differentiate between various designs when planning a survey, evaluate the potential gains from replacing an existing sample, and determine which non-responding units would contribute the most to enhancing the set of responding units.