Effective geographic sample size in the presence of spatial autocorrelation

As spatial autocorrelation latent in georeferenced data increases, the amount of duplicate information contained in these data also increases. This property suggests the research question asking what the number of independent observations, say n*, is that is equivalent to the sample size, n, of a data set. This is the notion of effective sample size. Intuitively speaking, when zero spatial autocorrelation prevails, n* = n; when perfect positive spatial autocorrelation prevails in a univariate regional mean problem, n* = 1. Equations are presented for estimating n* based on the sampling distribution of a sample mean or sample correlation coefficient with the goal of obtaining some predetermined level of precision, using the following spatial statistical model specifications: (1) simultaneous autoregressive, (2) geostatistical semivariogram, and (3) spatial filter. These equations are evaluated with simulation experiments and are illustrated with selected empirical examples found in the literature.