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Recent research has shown that two entropy-based segregation indices possess an appealing mixture of basic and subsidiary but useful properties. It would appear that the only fundamental difference between the mutual information or M index, and the entropy information or H index, is that the second is a normalized version of the first. This paper introduces another normalized index in that family, the H* index, which captures segregation as the tendency of racial groups to have different distributions across schools. More importantly, the paper shows that applied researchers may do better using the M index than using either H or H* in two circumstances: (1) if they are interested in the decomposability of the measurement of segregation, and (2) if they are interested in a margin-free measurement of segregation changes. The shortcomings of the H and H* indices are illustrated below by means of numerical examples, as well as with school segregation data by ethnic group in the U.S. public school system between 1989 and 2005.

An alternative measure of segregation, the P* index, is explained. This measure is computed separately for each racial/ethnic group and, in a diadic situation, indicates each group's potential for neighborhood contact with the other. The usefulness of this index, as well as the different information it provides from that provided by other indices, is discussed. P* indices are computed for blacks and whites for the St Louis metropolitan area in 1970 and 1980. The results indicate that neither group experienced a sizable increase in residential contact with the other between 1970 and 1980. The significance of this finding in a context of increasing black suburbanization is discassed.

Segregation is commonly measured by means of an index of dissimilarity. A recent 'boundary modified' version of the index was formulated. It was based upon the concept that segregation is a separation created by spatial structure imposed upon the social space and thus interaction between racial groups is limited. The index takes into account one of the spatial etements—contiguity—but ignores the others. This paper argues that the length of the common boundary between two areal units and the shape of the areal units are important spatial components in determining segregation. Thus, a family of segregation indices is derived by incorporating these spatial components and can be applied to various spatial configurations. One of the indices possesses a distinctive property which is useful for comparing segregation levels in regions of various scales.

The Fair Housing Act of 1968 made discrimination against minorities in the sale or rental of housing illegal. Twenty years later the Act's coverage was expanded and its enforcement mechanisms strengthened in response to pressure from fair housing advocates and evidence of continued segregation and discrimination. Segregation indices and fair housing audits provide measures of the extent and nature of residential segregation and housing discrimination. High levels of residential segregation suggest that housing discrimination exists, and audits give a direct measure of the incidence of discrimination. To date, housing audits consistently show that black auditors encounter discriminatory treatment in the housing search process. Whether the strengthened enforcement mechanisms of the Act will have a substantial impact on housing market discrimination and, in turn, residential segregation, remains to be seen.

Background: How can we compute a segregation or diversity index from a three-way or multi-way contingency table, where each variable can take on an arbitrary finite number of values and where the index takes values between zero and one? Previous methods only exist for two-way contingency tables or dichotomous variables. A prototypical three-way case is the segregation index of a set of industries or departments given multiple explanatory variables of both sex and race. This can be further extended to other variables, such as disability, number of years of education, and former military service. Methodology/Principal Findings: We extend existing segregation indices based on Euclidean distance (square of coefficient of variation) and Boltzmann/Shannon/Theil index from two-way to multi-way contingency tables by including multiple summations. We provide several biological applications, such as indices for age polyethism and linkage disequilibrium. We also provide a new heuristic conceptualization of entropy-based indices. Higher order association measures are often independent of lower order ones, hence an overall segregation or diversity index should be the arithmetic mean of the normalized association measures at all orders. These methods are applicable when individuals selfidentify as multiple races or even multiple sexes and when individuals work part-time in multiple industries. Conclusions/Significance: The policy implications of this work are enormous, allowing people to rigorously test whether employment or biological diversity has changed.

There has been extensive use of segregation indices for measuring residential segregation since 1950s, with continuous progress made in the field. Recent developments include the propositions of spatial global and local versions of traditionally used segregation indices, which have opened avenues for representing and analysing segregation as a multiscale and spatially varying phenomenon. Much less explored has been the issue of how important research design choices, such as the extent of geographical boundaries, grouping systems and scales of analysis, can influence the measurement of segregation. This paper contributes in this direction by investigating the impact of such decisions in the outcomes of the indices of generalized dissimilarity (D) and information theory (H) using a set of sensitivity analysis. Using a comparative study between London and São Paulo as basis, results obtained with different geographical boundaries, grouping systems and scales for the two indices are analysed visually and quantitatively. Results suggest that although D and H depict the same spatial dimension of segregation (unevenness/clustering), they present different sensitivity to geographical boundaries and grouping systems. The study also revealed how the two indices unfold different aspects of the segregation, which impact on their interpretation and applicability. The study concludes with a discussion of the considerations on research design choices concerning the interpretation of the results, which indicate the two indices should not be used interchangeably.

The aim of this article is to introduce a new stand-alone application—Geo-Segregation Analyzer—that is capable of calculating 43 residential segregation indices, regardless of the population groups or the metropolitan region under study. In practical terms, the user just needs to have a Shapefile geographic file containing counts of population groups that differ in ethnic origin, birth country, age, or income across a metropolitan area at a small area level (e.g., census tracts). Developed in Java using the GeoTools library, this free and open-source application is both multiplatform and multilanguage. The software functions on Windows, Mac OS X, and Linux operating systems and its user interface currently supports 10 languages (English, French, Spanish, Catalan, German, Italian, Portuguese, Creole, Vietnamese, and Chinese). The application permits users to display and manipulate several Shapefile geographic files and to calculate 19 one-group indices, 13 two-group indices, 8 multigroup indices, and 3 local measures that could be mapped (location quotient, entropy measure, and typology of the ethnic areas proposed by Poulsen, Johnson, and Forrest).