Statistical Analysis in the Presence of Spatial Autocorrelation: Selected Sampling Strategy Effects

Abstract

Fundamental to most classical data collection sampling theory development is the random drawings assumption requiring that each targeted population member has a known sample selection (i.e., inclusion) probability. Frequently, however, unrestricted random sampling of spatially autocorrelated data is impractical and/or inefficient. Instead, randomly choosing a population subset accounts for its exhibited spatial pattern by utilizing a grid, which often provides improved parameter estimates, such as the geographic landscape mean, at least via its precision. Unfortunately, spatial autocorrelation latent in these data can produce a questionable mean and/or standard error estimate because each sampled population member contains information about its nearby members, a data feature explicitly acknowledged in model-based inference, but ignored in design-based inference. This autocorrelation effect prompted the development of formulae for calculating an effective sample size (i.e., the equivalent number of sample selections from a geographically randomly distributed population that would yield the same sampling error) estimate. Some researchers recently challenged this and other aspects of spatial statistics as being incorrect/invalid/misleading. This paper seeks to address this category of misconceptions, demonstrating that the effective geographic sample size is a valid and useful concept regardless of the inferential basis invoked. Its spatial statistical methodology builds upon the preceding ingredients.