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Interpoint squared distance as a measure of spatial clustering
S Selvin1, J Schulman, D W Merrill
1Department of Biomedical and Environmental Health Sciences, University of California, Berkeley, CA 94720.
Social Science & Medicine (1982)
|April 1, 1993
Summary
This study introduces a new spatial clustering measure using mean interpoint squared distance. This method helps analyze spatial distributions, as demonstrated with non-Hodgkin
Area of Science:
- Spatial statistics
- Geographic information systems
- Epidemiology
Background:
- Analyzing spatial patterns is crucial in various scientific fields.
- Existing methods for spatial clustering may have limitations.
- Understanding spatial distributions can reveal underlying processes.
Purpose of the Study:
- To present the expectation and variance for the mean interpoint squared distance.
- To develop a novel measure for spatial clustering.
- To illustrate the application of this measure in analyzing disease spatial distribution.
Main Methods:
- Derivation of moments for a bivariate uniform distribution over an arbitrary polygon.
- Calculation of expectation and variance for mean interpoint squared distance.
- Exploration of the test statistic's distribution and power on the unit square.
- Application to a real-world case study of non-Hodgkin's lymphoma.
Main Results:
- Expressions for moments of bivariate uniform distributions are provided.
- The mean interpoint squared distance is established as a valid measure of spatial clustering.
- The distribution and power of the test statistic were analyzed.
- The approach was successfully applied to a small dataset of non-Hodgkin's lymphoma cases.
Conclusions:
- The mean interpoint squared distance offers a robust method for quantifying spatial clustering.
- The derived expressions facilitate the application of this statistical measure.
- This approach has potential applications in epidemiology and other spatial analyses.