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AJPH First Look, published online ahead of print Dec 27, 2005
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February 2006, Vol 96, No. 2 | American Journal of Public Health 205
© 2006 American Public Health Association
DOI: 10.2105/AJPH.2005.078857


LETTER

APPROPRIATE USE OF THE K FUNCTION IN URBAN ENVIRONMENTS

Seth Spielman, MS

Seth Spielman is with the Columbia University Graduate School of Architecture, Planning, and Preservation, New York, NY, and is a National Science Foundation IGERT Fellow in Geographic Information Science at the National Center for Geographic Information and Analysis, University of Buffalo, Buffalo, NY.

Correspondence: Requests for reprints should be sent to Seth Spielman, MS, 400 Avery Hall, Columbia University Graduate School of Architecture, Planning, and Preservation, New York, NY 10027 (e-mail: ses89{at}columbia.edu).

There is clearly a need to understand neighborhood food environments and how they contribute to behavior. "Clustering of Fast-Food Restaurants Around Schools: A Novel Application of Spatial Statistics to the Study of Food Environments"1 is an interesting approach to understanding this important need. However, the article raises a number of methodological concerns about the use of spatial statistics in urban environments.

First and foremost is that the planar K function, the statistical technique used by Austin et al., may not be appropriate for data derived from street addresses. The K function used employs an "as the crow flies" measure of distance. Children are not crows; they tend to navigate urban environments by means of streets and sidewalks. In cities, a straight-line measure of distance can dramatically underestimate the actual travel distance; thus, network-based K functions are more appropriate for urban analysis. Yamada and Thill found that using the planar K function with network-constrained point data leads to an overdetection of clusters; they suggested using network K functions as an alternative.2

Second, urban land use is generally regulated through zoning ordinances that dictate what can be located where. Modern zoning practice clusters like uses. The location of fast-food restaurants in Chicago is not a random process, so comparisons with complete spatial randomness are not meaningful. While K functions can be used effectively to detect clusters, interpreting the significance of the observed K function is tricky.

Austin et al. are unclear about the confidence intervals and how they were derived. They were based on simulations, but simulations of what? Restaurants can be located only in areas that are zoned appropriately. Confidence intervals, to be meaningful, should be based on simulations of random restaurant locations within the defined space of zones suitable for commercial fast-food establishments. A corollary concern is that the areas suitable for fast-food restaurants are clustered. A univariate K function examining only potential restaurant locations might help in determining whether fast-food restaurants are clustered.

Understanding how neighborhood characteristics relate to diet is critical work for public health and urban planning practitioners. I think the article by Austin et al. is an important contribution to understanding this relationship. However, it seems to me that the methods used in the study do not bear out the conclusions about clustering. A more careful application of the K function is required to answer questions about the spatial distribution of fast-food restaurants relative to schools.

References

1. Austin SB, Melly SJ, Sanchez BN, Patel A, Buka S, Gortmaker SL. Clustering of fast-food restaurants around schools: a novel application of spatial statistics to the study of food environments. Am J Public Health. 2005;95:1575–1581.[Abstract/Free Full Text]

2. Yamada I, Thill J-C. Comparison of planar and network k-functions in traffic accident analysis. J Transport Geography. 2004;12:149–158.[CrossRef]





This Article
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AJPH.2005.078857v1
96/2/205    most recent
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Right arrow Other Statistics/Evaluation/Research
Right arrow Urban Health


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