Error propagation in spatial modeling of public health data: a simulation approach using pediatric blood lead level data for Syracuse, New York

Soil Sample Assay Uncertainty and the Geographic Distribution of Contaminants: Error Impacts on Syracuse Trace Metal Soil Loading Analysis Results

A research team collected 3609 useful soil samples across the city of Syracuse, NY; this data collection fieldwork occurred during the two consecutive summers (mid-May to mid-August) of 2003 and 2004. Each soil sample had fifteen heavy metals (As, Cr, Cu, Co, Fe, Hg, Mo, Mn, Ni, Pb, Rb, Se, Sr, Zn, and Zr), measured during its assaying; errors for these measurements are analyzed in this paper, with an objective of contributing to the geography of error literature. Geochemistry measurements are in milligrams of heavy metal per kilogram of soil, or ppm, together with accompanying analytical measurement errors. The purpose of this paper is to summarize and portray the geographic distribution of these selected heavy metals measurement errors across the city of Syracuse. Doing so both illustrates the value of the SAAR software's uncertainty mapping module and uncovers heavy metal characteristics in the geographic distribution of Syracuse's soil. In addition to uncertainty visualization portraying and indicating reliability information about heavy metal levels and their geographic patterns, SAAR also provides optimized map classifications of heavy metal levels based upon their uncertainty (utilizing the Sun-Wong separability criterion) as well as an optimality criterion that simultaneously accounts for heavy metal levels and their affiliated uncertainty. One major outcome is a summary and portrayal of the geographic distribution of As, Cr, Cu, Co, Fe, Hg, Mo, Mn, Ni, Pb, Rb, Se, Sr, Zn, and Zr measurement error across the city of Syracuse.

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.