• Journal of the Korean Geographical Society
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• v.43 no.2
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• pp.253-262
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• 2008

The main objective of this paper is to formulate a generalized procedure to extract the first four moments of univariate spatial association measures for statistical testing under the normality assumption and to evaluate the viability of hypothesis testing based on the normal approximation for each of the spatial association measures. The main results are as follows. First, predicated on the previous works, a generalized procedure under the normality assumption was derived for both global and local measures. When necessary matrices are appropriately defined for each of the measures, the generalized procedure effectively yields not only expectation and variance but skewness and kurtosis. Second, the normal approximation based on the first two moments for the global measures fumed out to be acceptable, while the notion did not appear to hold to the same extent for their local counterparts mainly due to the large magnitude of skewness and kurtosis.

• Journal of the Korean Geographical Society
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• v.42 no.4
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• pp.616-631
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• 2007

Residential differentiation is an academic theme which has been given enormous attention in urban studies. This is due to the fact that residential segregation can be seen as one of the best indicators for socio-spatial dialectics occurring on urban space. Measuring how one population group is differentiated from the other group in terms of residential space has been a focal point in the residential segregation studies. The index of dissimilarity has been the most extensively used one. Despite its popularity, however, it has been accused of inability to capture the degree of spatial clustering that unevenly distributed population groups usually display. Further, the spatial indices of segregation which have been introduced to edify the problems of the index of dissimilarity also have some drawbacks: significance testing methods have never been provided; recent advances in spatial statistics have not been extensively exploited. Thus, the main purpose of the research is to devise a spatial separation measure which is expected to gauge not only how unevenly two population groups are distributed over urban space, but also how much the uneven distributions are spatially clustered (spatial dependence). The main results are as follows. First, a new measure is developed by integrating spatial association measures and spatial chi-square statistics. A significance testing method based on the generalized randomization test is also provided. Second, a case study of residential differentiation among groups by educational attainment in major Korean metropolitan cities clearly shows the applicability of the analytical framework presented in the paper.