Functions to calculate measures of spatial association, especially measures of spatial autocorrelation, have been made available in many software applications. Measures may be global, applying to the whole data set under consideration, or local, applying to each observation in the data set. Methods of statistical inference may also be provided, but these will, like the measures themselves, depend on the support of the observations, chosen assumptions, and the way in which spatial association is represented; spatial weights are often used as a representational technique. In addition, assumptions may be made about the underlying mean model, and about error distributions. Different software implementations may choose to expose these choices to the analyst, but the sets of choices available may vary between these implementations, as may default settings. This comparison will consider the implementations of global Moran's I, Getis-Ord G and Geary's C, local Ii and Gi, available in a range of software including Crimestat, GeoDa, ArcGIS, PySAL and R contributed packages.

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While the literature clearly acknowledges that individuals may experience different levels of segregation across their various socio-geographical spaces, most measures of segregation are intended to be used in the residential space. Using spatially aggregated data to evaluate segregation in the residential space has been the norm and thus individual's segregation experiences in other socio-geographical spaces are often de-emphasized or ignored. This paper attempts to provide a more comprehensive approach in evaluating segregation beyond the residential space. The entire activity spaces of individuals are taken into account with individuals serving as the building blocks of the analysis. The measurement principle is based upon the exposure dimension of segregation. The proposed measure reflects the exposure of individuals of a referenced group in a neighborhood to the populations of other groups that are found within the activity spaces of individuals in the referenced group. Using the travel diary data collected from the tri-county area in southeast Florida and the imputed racial-ethnic data, this paper demonstrates how the proposed segregation measurement approach goes beyond just measuring population distribution patterns in the residential space and can provide a more comprehensive evaluation of segregation by considering various socio-geographical spaces.

Segregation is commonly measured by means of an index of dissimilarity. A recent boundary modified' version of the index was formulated . It was based upon the concept that segregation is a separation created by spatial structure imposed upon the social space and thus interaction between racial groups is limited . The index takes into account one of the spatial elements-contiguity-but ignores the others . This paper argues that the length of the common boundary between two areal units and the shape of the areal units are important spatial components in determining segregation . Thus, a family of segregation indices is derived by incorporating these spatial components and can be applied to various spatial configurations. One of the indices possesses a distinctive property which is useful for comparing segregation levels in regions of various scales .

We recognized that many health outcomes are associated with air pollution, but in this project launched by the US EPA, the intent was to assess the role of exposure to ambient air pollutants as risk factors only for respiratory effects in children. The NHANES-III database is a valuable resource for assessing children's respiratory health and certain risk factors, but lacks monitoring data to estimate subjects' exposures to ambient air pollutants. Since the 1970s, EPA has regularly monitored levels of several ambient air pollutants across the country and these data may be used to estimate NHANES subject's exposure to ambient air pollutants. The first stage of the project eventually evolved into assessing different estimation methods before adopting the estimates to evaluate respiratory health. Specifically, this paper describes an effort using EPA's AIRS monitoring data to estimate ozone and PM10 levels at census block groups. We limited those block groups to counties visited by NHANES-III to make the project more manageable and apply four different interpolation methods to the monitoring data to derive air concentration levels. Then we examine method-specific differences in concentration levels and determine conditions under which different methods produce significantly different concentration values. We find that different interpolation methods do not produce dramatically different estimations in most parts of the US where monitor density was relatively low. However, in areas where monitor density was relatively high (i.e., California), we find substantial differences in exposure estimates across the interpolation methods. Our results offer some insights into terms of using the EPA monitoring data for the chosen spatial interpolation methods.