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Effective Geographic Sample Size in the Presence of Spatial Autocorrelation

Authors


School of Social Sciences, University of Texas at Dallas, P.O. Box 830688, GR31, Richardson, TX 75083-0688, e-mail: daniel.griffith@utdallas.edu.

Abstract

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 inline image, 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, inline image; when perfect positive spatial autocorrelation prevails in a univariate regional mean problem, inline image. Equations are presented for estimating inline image 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.

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