Reflections on the Dimensions of Segregation

Nancy Denton and I published “The Dimensions of Residential Segregation” in 1988, during the early phases of a multiyear project funded by the National Institute of Child Health and Human Development. The purpose of the project was to study the trends, patterns, causes, and consequences of racial and ethnic residential segregation the United States. Nancy was a postdoctoral research associate on the study at the time we began our investigation. In starting out, we encountered a vigorous debate in the literature about the “correct” or “right” way to measure neighborhood segregation that left us unsure about how to proceed methodologically.

Prior to the mid-1970s, however, the measurement of segregation had been settled science. In 1955, Otis Dudley Duncan and Beverly Duncan published an article in the American Sociological Review entitled “A Methodological Analysis of Segregation Indices,” in which they examined a variety of proposed measures. They concluded that the best overall measure was the Index of Dissimilarity (D), given its ease of computation, well-known and tractable properties, clear interpretation and invariance with respect to the relative number of minority group members. Over the ensuing two decades, a Pax Duncana ensued and D was widely used without debate as the standard measure of segregation. It comprised the main index for such classic works as Duncan and Duncan’s (1957) The Negro Population of Chicago, Taeuber and Taeuber’s (1965) Negroes in Cities, and Grebler et al.’s (1970) The Mexican-American People.

The Pax Duncana ended in 1976 with the publication of a critique by Cortese et al. entitled “Further Considerations on the Methodological Analysis of Segregation,” also published in the American Sociological Review. The article unleashed “a torrent of papers [that] considered a variety of definitions of segregation, proposed a host of new measures, and rediscovered several old indices” (Massey and Denton 1988:282). By the mid-1980s no consensus had been reached on how best to measure segregation and we uncovered some 20 different measures of the concept in our review of the literature. Before proceeding to the substance of our analysis, we decided we had to bring some order to the debate and so undertook a systematic analysis of segregation indices, resulting in the Social Forces paper.

We began by conceptually classifying measures with respect to five distinct dimensions of spatial variation: unevenness, exposure, clustering, concentration and centralization. Unevenness is the degree to which the percentage of minority group members within specific neighborhoods departs from the minority percentage in the entire urban area. Exposure is the degree of potential contact (or lack thereof) between minority and majority members within particular neighborhoods. Clustering is the extent to which minority neighborhoods adjoin one another in space. Concentration is the relative amount of physical space occupied by a minority group within a city; and centralization is the degree to which minority members settle in and around the social or geographic center of a metropolitan area.

After defining the indices mathematically and classifying them conceptually, we assembled data for the nation’s largest metropolitan areas in 1980, computed index values for Hispanics, Blacks and Asians across all 20 measures, and factor analyzed the resulting set of indices to reveal their underlying factor structure. We obtained a factor pattern matrix that yielded a robust interpretation across different rotation and extraction methods, one that confirmed the conceptual structure we had hypothesized. Based on our analysis of the indices and our reading of the extant literature, we recommended an optimal measure for each dimension: the dissimilarity index for unevenness; the P* index for exposure; the spatial proximity index for clustering; the relative concentration index for concentration; and the absolute centralization index for centralization. The analysis and its conclusions were later replicated using a larger data set compiled for the 1990 census (see Massey, White and Phua 1996).

In our Social Forces paper, Nancy and I argued that social scientists should stop fighting about which measure of segregation was “best” or most “correct,” and instead measure all dimensions simultaneously to see what a multidimensional assessment might reveal about the nature of segregation in U.S. society. We then undertook this exercise for...