Measuring global spatial autocorrelation with data reliability information.

Assessing spatial autocorrelation (SA) of statistical estimates such as means is a common practice in spatial analysis and statistics. Popular spatial autocorrelation statistics implicitly assume that the reliability of the estimates is irrelevant. Users of these SA statistics also ignore the reliability of the estimates. Using empirical and simulated data, we demonstrate that current SA statistics tend to overestimate SA when errors of the estimates are not considered. We argue that when assessing SA of estimates with error, it is essentially comparing distributions in terms of their means and standard errors. Using the concept of the Bhattacharyya coefficient, we proposed the Spatial Bhattacharyya coefficient (SBC) and suggested that it should be used to evaluate the SA of estimates together with their errors. A permutation test is proposed to evaluate its significance. We concluded that the SBC more accurately and robustly reflects the magnitude of SA than traditional SA measures by incorporating errors of estimates in the evaluation.