There are many ways to measure how clustered, or segregated, data are. Often, we want to measure housing segregation or school segregation; numerous indexes can turn all the data into one number between zero and one, between minimum and maximum segregation.
Massey and Denton (1988) looked at many of these segregation indexes and argued that segregation encompasses five distinct dimensions of spatial variation: evenness, exposure, clustering, concentration, and centralization. These findings were updated using 1990 census data by Massey, White, and Phua (1996), and by Wilkes and Iceland (2004) for the year 2000.
The Theil (1972) entropy index is a comprehensive measure of segregation related to inequality measures. The entropy index can also be expanded to measure segregation across two or more variables simultaneously (e.g., race/ethnicity and income), and can be assigned to portions due to each variable and interaction (Fischer 2003; White 1986).
The index of clustering Massey and Denton recommended is the White (1983) index of spatial proximity, a weighted average of the average distance between members of the same group and the average distance between members of different group. White (1984) also proposed using squared distances, which yields the proportion of spatial variance explained.
Fischer, Mary J. 2003. “The Relative Importance of Income and Race in Determining Residential Outcomes in U.S. Urban Areas 1970-2000.” Urban Affairs Review 38: 669–96.
Massey, Douglas S., and Nancy A. Denton. 1988. “The Dimensions of Residential Segregation.” Social Forces 67: 281–315.
Massey, Douglas S., Michael J. White, and Voon-Chin Phua. 1996. “The Dimensions of Segregation Revisited.” Sociological Methods and Research 25: 172–206.
Theil, Henri. 1972. Statistical Decomposition Analysis. Amsterdam: North Holland.
White, Michael J. 1983. “The Measurement of Spatial Segregation.” American Journal of Sociology 88: 1008–19.
———. 1984. “Reply to Mitra.” American Journal of Sociology 90: 189–91.
———. 1986. “Segregation and Diversity: Measures in Population Distribution.” Population Index 52: 198–221.
Wilkes, Rima, and John Iceland. 2004. “Hypersegregation in the Twenty-First Century.” Demography 41: 23–36.