Using U.S. Census Bureau data and geographies, I've computed a Relative Rurality Index for almost 11,000 U.S. school districts. The index is calculated based on the distance between centroids of each district and the nearest urban cluster with a population of fifty thousand or greater, the population density of the county in which the district is located, and the population decline of the same county (2010-2018), each scaled to the national extrema and composited with more weight given to remoteness (scaled distance from nearest urban area) and sparseness (inverse of scaled population density). The aim here is to develop a basis for intranational comparisons within and across studies as well as for site selection and recruitment. Initial results seem promising.
The index was compiled using custom Python scripts relying heavily on the bindings for OSGEO's OGR library. The maps, previews of which appear above, are generated using my custom vector rendering package vfr. The projection is the U.S. National Atlas Equal Area projection (EPSG:2163).
The key products are a detailed index file and a summary file. The detailed index file contains one row for each school district, its rurality index, the component indices, and additional useful data as in the excerpt below (taken from around the median). The summary file contains national and state-level extrema and statistics. Optionally, a shapefile is also generated, identical to the U.S. Census Bureau UNSD product but augmented with the Rurality Index and its component indices.