A Hypothesis Test for Detecting Distance-Specific Clustering and Dispersion in Areal Data

Area of Science:

• Spatial statistics
• Geographic information systems (GIS)
• Environmental science

Background:

• Spatial clustering detection is vital across diverse fields, from epidemiology to neuroscience.
• Ripley's K-function is a standard for point process data but less adapted for areal data.
• Accurate assessment of spatial patterns in areal data remains a challenge.

Purpose of the Study:

• To develop a novel method for detecting spatial clustering and dispersion in areal data.
• To introduce the positive area proportion function (PAPF) inspired by Ripley's K-function.
• To evaluate the performance of the PAPF hypothesis test against existing spatial statistics.

Main Methods:

• Development of the positive area proportion function (PAPF) for areal data analysis.
• Creation of a hypothesis testing procedure based on the PAPF.
• Comparison of PAPF test with global Moran's I, Getis-Ord G, and spatial scan statistics via simulations.
• Real-world application to land parcels and county-level health data.

Main Results:

• The PAPF provides a new approach for spatial clustering detection in areal data.
• Simulation studies demonstrate the performance of the PAPF test.
• Real-world analyses successfully identified spatial clustering in conservation easements and pediatric overweight/obesity rates.

Conclusions:

• The positive area proportion function (PAPF) offers a valuable tool for spatial clustering analysis of areal data.
• The PAPF hypothesis test is a viable alternative to existing methods for specific spatial analyses.
• This method has practical implications for understanding geographic distributions in various domains.