A set of associated statistical tests for spatial clustering |
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Authors: | Email author" target="_blank">Peter A?RogersonEmail author |
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Institution: | (1) Departments of Geography and Biostatistics and National Center for Geographic Information and Analysis, , University at Buffalo, Wilkeson Hall, Buffalo, NY 14261, USA |
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Abstract: | The purpose of this paper is to develop a set of associated statistical tests for spatial clustering. In particular, a set
of three associated tests will be developed; these will correspond to the three types of tests set out by Besag and Newell
(general tests, focused tests, and tests for the detection of clustering). The associated tests draw primarily, though not
exclusively, upon existing tests and results. The principal contributions are based upon the score statistic for focused tests,
which has been an important approach to testing for clustering around environmental hazards. The first contribution consists
of the formulation of a global statistic for general tests that corresponds to focused score statistics, along with an assessment
of the distribution of the statistic under the null hypothesis of no raised incidence. The local score statistics used for
focused tests will have the property of summing to the global statistic used for the corresponding general test. Attention
is also given to the maximum local score statistic for the “test for the detection of clustering”. The critical values of
this statistic which are required for testing the null hypothesis are described. Application of the methods is made to leukemia
data for central New York State. |
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Keywords: | global and local statistics general tests focused tests maximum local statistic |
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