Encyclopedia of SociologyVol._4

ment to uphold the law in this instance finally communicated to black people and some whites that the existence of segregation had corrupted not just local public officials but even officials of the federal government. The fight had to begin at the top.

The next major chapter in the effort to desegregate the South took place in Albany, Georgia, in 1961. Failing in their desegregation efforts there, King and the SCLC launched a new project to protest segregated lunch counters in downtown Birmingham, Alabama. King was jailed. While in jail, he wrote his philosophically brilliant ‘‘Letter from a Birmingham Jail.’’ Although Birmingham’s white business leaders agreed on a desegregation plan, King’s motel was still bombed. Medgar Evers was shot to death in neighboring Jackson, Mississippi, and four young children were murdered in the bombing of the Sixteenth Street Baptist Church in Birmingham. Blacks learned that even if they could get local public officials and businessmen to change segregationist policies, some Southern whites, perhaps even the majority, would not accept change. They also learned that among the majority there were those who were willing to use violence. Blacks had to have protection from another source.

In 1964, the Student Nonviolent Coordinating Committee (SNCC) began its Freedom Summers Project in Mississippi. Mississippi was considered by blacks the most dangerous state in the South, and it lived up to its reputation. On Sunday, August 4, 1964, Mississippi claimed the lives of James Chaney, Michael Swerner, and Andrew Goodman—the latter two were white. All three were members of SNCC’s Freedom Summer Project. Their only offense was that they had volunteered to teach black youth, work with the rural poor, and register blacks to vote. If it was not apparent during the Freedom Rides, it was now apparent that Southern whites would kill anybody, whites included, who opposed their way of life.

Blacks now had a growing collection of concerned Northern whites. Swerner’s wife commented that it was unfortunate, but apparently whites had to die before other, complacent whites would listen. The parents of the two young white students, Swerner and Goodman, talked about the martyrdom of their children. They were proud but grief-stricken. They insisted that the monstrous

evil of segregation must be destroyed. Black members of the Congress of Racial Equality (CORE) and SNCC were furious. Some of them had been personal friends of James Chaney, who was black. They blamed the governor of the state and the federal government for what happened in Philadelphia, Mississippi, during the summer of 1964.

As a result of those murders, SNCC and SCLC mobilized a march to Montgomery. Near the end of their march, however, they were attacked by mounted sheriff’s officers wielding clubs. Men and women, as well as young adults and children, were beaten.

In summary, the central focus of black struggle in the South from 1955 to 1965 was desegregation. Blacks insisted on desegregating public transportation facilities, public eating establishments, public water fountains, public bathrooms, and public institutions of higher education. As a result of the violence they experienced, black Southerners learned that desegregation required more than protests, it required changes in the law at the national level. A civil-rights bill was required. Certainly a change in the law was required, but even that was not enough. In order for changes to be implemented, government officials had to demonstrate a willingness to protect and defend the rights of African Americans.

It was not long after Selma that Watts, an urban ethnic enclave near Los Angeles, exploded, beginning a series of race riots that developed spontaneously throughout the latter half of the 1960s. Stores were torched and looted. Surveying the destruction in Watts, Dr, King and SCLC decided that it was time to take their movement north. What they were not aware of was that their desegregation strategies would not solve the problems of Northern blacks, because the central problem for that group was not segregation. To understand this, it is necessary to contrast the evolution of the black middle class in the South with that in the North.

DESEGREGATION VERSUS INTEGRATION

A biracial system similar to that in the South never surfaced in the American North. As a result, blacks there depended almost completely on whites for employment. Northern whites, furthermore, had not come to depend on black labor, with the

possible exception of domestic labor. Domestic labor, however, did not produce wealth; it was a symbol of surplus wealth. In addition, Northern whites who wanted to remain physically (residentially) separated from blacks did not feel any need to employ them, with the exception of menial labor jobs. With the influx of European immigrants, Northern whites preferred to hire the sons and daughters of Europe rather than the emancipated slaves of the South (Blauner 1972; Jones 1985). Indeed, from the turn of the century to the beginning of World War II. Northern blacks never established a foothold in the manufacturing industries of the North ( Jones 1985). According to Blauner, even in ancillary industries such as meatpacking where blacks initially gained a foothold because of the unhealthy working conditions they were actually displaced by European immigrants during the 1930s.

Given their background, the problem for the black middle class in the North was different from that for the black middle class in the South, and the leadership of the civil-rights movement knew it. At one point, Dr. King said that ‘‘the struggles of the past decade were not national in scope; they were Southern; they were specifically designed to change life in the South’’ (1968, p. 70). Northern blacks had only been segregated (de facto) residentially. Otherwise they could ride public transportation and eat at many of the major restaurants, although it was understood that some owners would discourage blacks from coming by being discourteous. The major concern of Northern mid- dle-class blacks, therefore, was not formal desegregation but discrimination and unequal access. They insisted that they should get the same quality of goods or service for their money. Their major concern was reflected in their insistence on greater job opportunities. They rejected the idea of caste barriers in employment, and they insisted that promotions be tied fairly to evaluation, irrespective of race. They rejected job ceilings and the idea of determining job status on the basis of race. These kinds of problems could not be solved by civil rights marches. They could not be solved simply by desegration or changing the law. Such changes would help, perhaps, but what was required was to get the federal government to establish civil-rights policies that would declare such acts as violations of the law and then, even more important, connect those policies to some kind of

enforcement device so that private corporations and governmental agencies would comply with the law. This is exactly what the Civil Rights Act of 1964 in combination with affirmative action, did.

THE FAILURE OF INTEGRATION:

THE URBAN POOR

Soon after the Civil Rights Act was passed by Congress and signed by President Lyndon B. Johnson, Executive Orders 11246 and 11375 were issued. Those orders led to the policy of affirmative action (Black 1981). Affirmative action policies essentially required that all city, state, and federal agencies, as well as any private corporation that contracted with the federal government, make every reasonable attempt to increase the proportion of minority workers in their workforces. Affirmative action was to be a device to address the effects of past discrimination. It did not take long to realize, however, that mostly middle-class blacks were benefiting from affirmative-action policies (Wilson 1987). The reason for this was twofold. First, middle-class blacks were the only ones who had competitive resources (such as skills they had acquired from higher education), owned businesses, or had parents who as a result of their professional status (doctors, dentists, ministers, etc.) were able to provide a competitive advantage for their children. Second, the American economy underwent structural changes that created more opportunities for professional, technical, human service, and clerical staff. As these opportunities increased, affirmative-action policies increased the likelihood that some of those jobs would go to black Americans. It was not long, however, before it also became apparent that neither affirmative-action policies nor the structural shift in the economy would aid black Americans who were poor and unskilled. In fact, as the economy shifted from a majority of manufacturing industries to a majority of service industries, a segmented labor market developed. A segmented labor market generated differential rates of mobility for differing class segments of the same group (Wilson 1978; 1981; 1987).

It is not surprising that when Mayor Richard Daly of Chicago and Martin Luther King, Jr., met early in 1966 and King complained about the slum housing of poor blacks in that city, Daly responded, ‘‘How do you expect me to solve the problems of

poverty and joblessness overnight?’’ King had no answer. He would quickly leave Chicago and the North after unsuccessful attempts both to help the impoverished and to desegregate Cicero, Illinois. It is to Dr. King’s credit, however, that he recognized that the problems of the poor had not been solved and that a Poor People’s Campaign was required.

Oblivious to the needs of the poor in the black community, Northern blacks who had turned a desegregationist movement into an integrationist movement (those Sowell [1984] incorrectly labels as people with a civil-rights vision) pursued integration with a vengeance. When the Civil Rights Act of 1964 became the law of the land, affirmative action was to be its guiding policy and equal opportunity and equal access the measure of fairness. It was not long, however, before civil-rights advocates recognized that something was amiss not only for the Northern black poor but also for the middle class. For example, although data from the 1970 census showed that black male college graduates in 1969 received a slightly higher average income than did comparable whites, other data demonstrated that the majority of black college students did not graduate from college. In fact, when Fleming (1985) researched this issue and compared the performance of black colleges with limited resources to that of predominantly white urban universities with considerably more resources that attracted black students with higher SAT scores, she found that the black colleges produced more intellectual and psychosocial development among black students than did the white colleges. Further, she found that typically white colleges produced ‘‘academic deterioration’’ among black students and concluded that better facilities and more institutional resources do not necessarily translate into a higher-quality college or university education (Fleming 1985. p. 186). She added that similar findings were reported in desegregated or so-called integrated public schools (Knowles 1962).

The fact is that whether or not schools are integrated, the situation confronting black children in most Northern and Southern public schools is catastrophic. Indeed, for the most part integration has failed black children. Once they enter school, they fall quickly behind their white counterparts on most measures of intelligence and scholastic achievement (Coleman 1966; Denton

1981). In fact, the longer black children remain in school, the further they fall behind. Denton (1981) reports that compared to white children, black children are three times as likely to be labeled mentally retarded, twice as likely to be suspended for discipline and attendance problems, and twice as likely to drop out of high school (White 1984, pp. 102–103). Black students who remain in school on average are two to three years below grade level in the basics—reading, writing, and arithmetic.

Educational integration consequently has often led to less growth and, even worse, the actual deterioration of the academic potential of black students in institutions of higher education. In those situations where deterioration does not actually occur, stagnation does (Black 1981).

These kinds of problems compound in later life such that black students have only ‘‘half as much . . . chance as a white child of finishing college and becoming a professional person,’’ twice as much chance of being unemployed, and a one in ten chance of getting in trouble with the law (and, if these students are young males, a one in four chance of involvement with the criminal justice system); finally, as they age, black students have a life expectancy that is five years shorter than that of white adults (White 1984, p. 103).

Without an adequate education, black males become less employable, less marriageable, and more criminal.

Wilson (1981, 1987) examined the combined indicators of unemployment rates, labor-force participation rates, employment-population ratios, and work experience and concluded that not only do these indicators reveal a disturbing picture of joblessness, they also indicate that a growing percentage of young black males are not marriageable, that is, cannot contribute to the support of a family. Examining rates of teenage pregnancy; crime and violence, especially homicide; and increases in substance abuse, Wilson argues that many of these young men are more likely to become predators than responsible workers.

Further, according to Wilson, poverty has compounded in black urban ethnic enclaves. He demonstrates that there has been a significant increase in what he refers to as extreme poverty areas (i.e., areas with a poverty rate of at least 40 percent) in the black urban ethnic enclave. Wilson contrasts

the growth of these areas with low-poverty areas (census tracts with a poverty rate of at least 20 percent) and high-poverty areas (with a poverty rate of at least 30 percent). The number of extreme poverty areas, he emphasizes, increased by a staggering 161 percent.

Wilson also demonstrates that the black community is losing its vertical class integration. Black middle-class and stable working-class families are choosing to live in the suburbs, and as they do, the institutions they used to staff, support, and nourish decline in number and importance.

The eventual demise of ethnic enclaves in urban areas has been experienced by all ethnic groups in America; for Europeans the process has taken from four to six generations. For blacks the process began in the late 1960s and early 1970s. Of course there was resistance to residential integration, as mirrored in the hostility that exploded in Cicero, Illinois, in the 1960s, and it continued in the 1990s. Although blacks residing in white suburbs are often racially harassed, residential integration is gaining momentum even as some whites move out of suburbia to exurbia or back to the city.

It should be noted, however, that the process of ethnic enclave decline for blacks is fundamentally different from that for European ethnics. Europeans settled in urban areas at a time when urban job opportunities were increasingly plentiful. Most of the jobs were in manufacturing and did not require skilled labor. And since Europeans were preferred over blacks, the sheer numbers of jobs allowed them to lift a whole mass of people out of squalor. As economic stability increased, European ethnics began the process of preparing themselves for increased mobility within the American occupational structure. To do this, education was critical—educational institutions are essentially preparatory institutions. In sum, the occupational and economic success of European ethnics required a stable economic base first, education second, and occupational success third (Greeley 1976). The circumstances of black Americans (a sizable segment of whom were denied stable employment opportunities in the North) were totally different, particularly in urban areas and especially in the North.

European ethnics were preferred over black laborers. Consequently, while European ethnics

were reaping the benefits of full employment, blacks were denied equal access to the labor market, undermining their ability to establish a stable economic base. And for those who would come later, after manufacturing jobs actually began to diminish because of the restructuring of the economy, there world be nothing but long-term unemployment. These groups would eventually form the black underclass as one generation of unemployed workers would quickly give rise to another. European ethnics were described by the sociologists of the 1920s and 1930s as socially disorganized (Thomas and Zananiecki 1927). Their communities were plagued by crime, delinquency, gangs, prostitution, and filth, but the availability of employment opportunities in the 1940s and 1950s allowed many to ‘‘lift themselves up by their own bootstraps.’’

The jobs that are available to blacks now because of the growth in the service sector of the American economy are either jobs that do not pay enough for a person to support a family or require considerable education and training, and so black urban ethnic enclaves are likely to undergo a different kind of transformation than did the European ethnic enclaves of the early 1900s. The middle class will be increasingly siphoned off from such enclaves, leaving behind a large residue of the most despondent and dependent, the most impoverished, the most violent, and the most criminal elements. Without new institutions to play the role of surrogate parents, without some kind of mandatory civilian social service corps, blacks in those communities may become a permanent underclass. A residue was also left behind by European ethnics, but it was much smaller and therefore much less problematic. As the black middle class leaves, it leaves its ethnic community devoid of the leadership or resources needed to regain its health. And as the numbers of female-headed families increase, the middle class will eventually have left the majority of black people behind. Integration, then, has undermined the health and the integrity of the black community.

The counterposition is now being proffered by many people, organizations, and school systems throughout the United States. This can be seen in the proliferation of segregated black programs where black youngsters are being taught only by black teachers. In this context, race clearly

is the critical issue. Gender however, has also become an issue. In many of these schools, black males insist that only they can do the job. Since black women have had to bear the burden of rearing children alone for so long, there is no doubt that they can use some help. One critical problem remains for people of this persuasion, however, and that is the continuing trend of black middle-class and stable working-class flight. Can the black community stem the tide? It is not suggested here that the black middle class can solve the problem alone but rather that it must provide the leadership, as it did in the segregated black institutions of the South, and that government must pay for it. Can the exodus be diminished?

Possibly, the passage of anti-affirmative action legislation and the increased reliance on standardized testing in higher education may alert the black middle class that the opportunities for their children are diminishing. Already they are starting to send their children to historically black colleges and universities in record numbers. This is a major shift in black higher education, and the number of available admissions is limited. As their children’s opportunities decrease, maybe they will come to see that in America the opportunities of black Americans will always be dependent upon the amount of pressure that blacks as a people can bring to bear on the system.

In the last few months of 1998, several antiaffirmative action programs were passed—Propo- sition 209 in California and Initiative 200 in Washington, for example. These initiatives were passed despite the demonstrated benefits of affirmative action for the broader society.

College and University Admissions. Princeton N.J.: Princeton University Press.

Blauner, Robert 1972 Racial Oppression in America. New York: Harper and Row.

Bonacich, Edna 1972 ‘‘A Theory of Ethnic Antagonism: The Split Labor Market.’’ American Sociological Review 37 (October): 547–559.

Coleman, James S. 1966 Equality of Educational Opportunity. Washington, D.C.: U.S. Government Printing Office.

Denton, Herbert 1981 ‘‘Future Still Bleak for Black Children, Lobbying Group’s Statistics Show.’’ Los Angeles Times, January 14(1A):4.

Fleming, Jacqueline 1985 Blacks in College. San Fran-

cisco: Jossey-Bass.

Franklin, John Hope 1947 From Slavery to Freedom: A History of Negro Americans, 4th ed. New York: Knopf.

Greeley, Andrew M. 1976 ‘‘The Ethnic Miracle.’’ The Public Interest 45: 20–36.

Jones, Jacqueline 1985 Labor of Love, Labor of Sorrow: Black Women, Work and the Family, From Slavery to the Present. New York: Vintage.

——— 1998 American Work: Four Centuries of Black and White Labor. New York: Norton.

King, Martin Luther, Jr. 1968 Where Do We Go From Here: Chaos or Community? Boston: Beacon Press.

Knowles, L. W. 1962 ‘‘Part 1, Kentucky.’’ In United States Commission on Civil Rights, Civil Rights USA: Public Schools, Southern States. Washington, D.C.: U.S. Government Printing Office.

Krombowski, John A., ed. 1991 Annual Edition: Race and Ethnic Relations, 91 to 92. Guilford, Conn.: Dushkin.

Massey, Donald, and Nancy Denton 1993 American Apartheid: Segregation and the Making of the Under-class. Cambridge, Mass.: Harvard University Press.

Raines, Howell 1977 My Soul Is Rested. New York: Penguin.

(SEE ALSO: Apartheid; Discrimination; Equality of Opportunity; Ethnicity; Prejudice; Race; Segregation and Desegregation; Slavery and Involuntary Servitude)

REFERENCES

Black, Albert N., Jr. 1977 ‘‘Racism Has Not Declined, It Has Just Changed Form.’’ Umojo 1, no. 3 (fall).

——— 1981 ‘‘Affirmative Action and the Black Academic Situation.’’ Western Journal of Black Studies 5:87–94.

Bowen, William, G., and Derek Bok 1998 The Shape of the River: Long-Term Consequences of Considering Race in

Scott, Joseph W. 1977 ‘‘Afro-Americans as a Political Class: Towards Conceptual Clarity.’’ Sociological Focus 10 (4):383–395.

Sowell, Thomas 1984 Civil Rights: Rhetoric or Reality? New York: Morrow.

Thomas, William I., and Florian Zananiecki 1927 The Polish Peasant in Europe and America. New York: Alfred A. Knopf.

Van den Berghe, Pierre L. 1967 Race and Racism: A Comparative Perspective. New York: Wiley.

White, Joseph 1984 The Psychology of Blacks: An AfroAmerican Perspective. Englewood Cliffs, N.J.: Pren- tice-Hall.

Wilson, William J. 1978 ‘‘The Declining Significance of Race: Revisited but Not Revised.’’ Society, vol. 15.

———1981 ‘‘The Black Community in the 1980s: Questions of Race, Class, and Public Policy.’’ Annals of the American Academy of Political and Social Science, vol. 454.

———1987 The Truly Disadvantaged: The Inner City, Underclass, and Public Policy. Chicago: University of Chicago Press.

———1996 When Work Disappears: The World of the New Urban Poor. New York: Vintage.

ALBERT WESLEY BLACK, JR.

SEGREGATION INDICES

Residential segregation has been a prominent topic in sociology since Burgess (1928) published his landmark study more than seventy years ago, and for almost as long, sociologists have argued about how to measure it. The debate has ebbed and flowed, and for a time the issue seemed to have been settled. In 1955, Duncan and Duncan published a landmark article (Duncan and Duncan 1955) demonstrating that there was little information in any of the prevailing indices that had not been captured already by the index of dissimilarity. For twenty years afterward, that measure was employed as the standard index of residential segregation.

This Pax Duncanae came to an abrupt end in 1976 with the publication of a critique of the dissimilarity index by Cortese and colleagues, ushering in a period of debate that has not ended (Cortese et al. 1976). Over the ensuing decade, a variety of old indices were reintroduced and new ones were invented, yielding a multiplicity of candidates. In an effort to bring some order to the field, Massey and Denton (1988) undertook a systematic analysis of twenty segregation indices they had identified from a review of the literature. They argued that segregation is not a unidimensional construct but encompasses five distinct dimensions of spatial variation. No single dimension is intrinsically more ‘‘correct’’ than any other; each reflects a different facet of the spatial distribution of social groups.

The five dimensions they identified are evenness, exposure, clustering, concentration, and cen-

tralization. To verify that conceptualization, Massey and Denton (1988) carried out a factor analysis of indices computed from 1980 census data for U.S. metropolitan areas. Their results showed that each index correlated with one of five factors corresponding to the dimensions they postulated. On theoretical, empirical, and practical grounds, they selected a single ‘‘best’’ indicator for each dimension of segregation. The dimensional structure of segregation and Massey and Denton’s (1988) selection of indices have been reaffirmed using 1990 census data (Massey et al. 1996).

The first dimension of segregation is evenness, which refers to the unequal distribution of social groups across areal units of an urban area. A minority group is segregated if it is unevenly spread across neighborhoods. Evenness is not measured in an absolute sense but is scaled relative to another group. It is maximized when all areal units have the same relative number of minority and majority members as the city as a whole and is minimized when minority and majority members have no areas in common.

The index of dissimilarity quantifies the degree of departure from an even residential distribution. It computes the number of minority group members who would have to change neighborhoods to achieve an even distribution and expresses that quantity as a proportion of the number that would have to change areas under conditions of maximum unevenness. The index varies between zero and one, and for any two groups X and Y it is computed as:

where xi and yi are the number of group X and group Y members in areal unit i and X and Y are the number of group X and group Y members in the city as a whole, which is subdivided into n areal units.

Among its properties, the index is inflated by random factors when the number of minority group members is small relative to the number of areal units (Cortese et al. 1976). It is also insensitive to the redistribution of minority group members among areal units with minority proportions above or below the city’s minority proportion

( James and Taeuber 1985; White 1986). Only transfers of minority members from areas where they are overrepresented (above the city’s minority proportion) to areas where they are underrepresented (below the minority proportion) affect the value of the index.

The property means that the dissimilarity index fails the ‘‘transfers principle,’’ which requires that segregation be lowered whenever minority members move to areas where they constitute a smaller proportion of the population. This and other problems led James and Taeuber (1985) to recommend using another measure of evenness, the Atkinson index (Atkinson 1970). Massey and Denton (1988), however, pointed out that the Atkinson index and dissimilarity indices are highly correlated and generally yield the same substantive conclusions. Moreover, the Atkinson index is actually a family of indices, each of which gives a slightly different result, creating problems of comparability. Given that D has been the standard index for more than thirty years, that its use has led to a large body of findings, and that that index is easy to compute and interpret, Massey and Denton (1988) recommended using it to measure evenness in most cases.

White (1986) points out, however, that another index may be preferred in measuring segregation between multiple groups, since the dissimilarity index is cumbersome to compute and interpret when the number of groups exceeds two. Thus, if one wants to generate an overall measure of segregation between ten ethnic groups, separate dissimilarity indices will have to be computed between all possible pairs of groups and averaged to get a single measure. An alternative index is Theil’s (1972) entropy index, which yields a single comprehensive measure of ethnic segregation. The entropy index also can be expanded to measure segregation across two or more variables simultaneously (e.g. ethnicity and income) and can be decomposed into portions attributable to each of the variables and their interaction (see White 1986).

The second dimension of segregation is exposure, which refers to the degree of potential contact between groups within the neighborhoods of a city. Exposure indices measure the extent to which groups must physically confront one another because they share a residential area. For

any city, the degree of minority exposure to the majority is defined as the likelihood of having a neighborhood in common. Rather than measuring segregation as a departure from an abstract ideal of ‘‘evenness,’’ however, exposure indices get at the experience of segregation from the viewpoint of the average person.

Although indices of exposure and evenness are correlated empirically, they are conceptually distinct because the former depend on the relative size of the groups that are being compared, while the latter do not. Minority group members can be evenly distributed among the residential areas of a city but at the same time experience little exposure to majority group members if they constitute a relatively large share of the population of the city. Conversely, if they constitute a small proportion of the city’s population, minority group members tend to experience high levels of exposure to the majority regardless of the level of evenness. Exposure indices take explicit account of such compositional effects in determining the degree of segregation between groups.

The importance of exposure was noted early by Bell (1954), who introduced several indices. However, with the establishment of the Pax Duncanae in 1955, sentiment coalesced around the dissimilarity index and exposure was largely forgotten until Lieberson reintroduced the P* index in the early 1980s (Lieberson 1980, 1981). This index has two basic variants. The interaction index (xP*y) measures the probability that members of group X share a neighborhood with members of group Y, and the isolation index (xP*x) measures the probability that group X members share an area with each other.

The interaction index is computed as the mi- nority-weighted average of each neighborhood’s majority proportion:

where xi, yi, and ti are the numbers of group X members, group Y members, and the total population of unit i, respectively, and X represents the number of group X members citywide. The isolation index is computed as the minority-weighted average of each neighborhood’s minority proportion:

Both indices vary between zero and one and give the probability that a randomly drawn group X member shares a neighborhood with a member of group Y (in the case of xP*y) or with another group X member (in the case of xP*x). Values of yP*x and yP*y can be computed analogously from equations (2) and (3) by switching the x and y subscripts. When there are only two groups, the isolation and interaction indices sum to one, so that xP*y + xP*x = 1.0 and yP*x + yP*y = 1.0. The interaction indices are also asymmetrical; only when group X and group Y constitute the same proportion of the population does xP*y equal yP*x.

P* indices can be standardized to control for population composition and eliminate the asymmetry (Bell 1954; White 1986). Standardizing the isolation index yields the well-known correlation ratio, or eta2 (White 1986). Stearns and Logan (1986) argue that eta2 constitutes an independent dimension of segregation, but Massey and Denton (1988) hold that it straddles two dimensions. Since it is derived from P*, eta2 displays some properties associated with an exposure measure, but standardization also gives it the qualities of an evenness index. Massey and Denton (1988) demonstrate this duality empirically and argue that it is better to use D and P* as separate measures of evenness and exposure. Nonetheless, Jargowsky (1996) has shown that one version of eta2 yields a better and more concise measure of segregation when one wishes to measure segregation between multiple groups simultaneously (e.g., between income categories).

The third dimension of segregation is clustering, or the extent to which areas inhabited by minority group members adjoin one another in space. A high degree of clustering implies a residential structure in which minority areas are arranged contiguously, creating one large enclave, whereas a low level of clustering means that minority areas are widely scattered around the urban environment, like a checkerboard.

The index of clustering recommended by Massey and Denton (1988) is White’s (1983) index of spatial proximity, SP. It is constructed by calculating the average distance between members of

the same group and the average distance between members of different groups and then computing a weighted average of those quantities. The average distance, or proximity, between group X members is

and the average proximity between members of group X and group Y is

where Y is the number of group Y members citywide, xi and yj are the numbers of group X and group Y members in units i and j, and cij is a distance function between these two areas, defined here as a negative exponential: cij = exp (−dij). The term dij represents the linear distance between the centroids of units i and j, and dij is estimated as (.6ai) 5, where ai is the area of the spatial unit. Use of the negative exponential implicitly assumes that the likelihood of interaction declines rapidly as the distance between people increases.

Average proximities also may be calculated among group Y members (Pyy) and among all members of the population (Pu) by analogy with equation (4). White’s SP index (1983) represents the average of intragroup proximities, Pxx,/Ptt and Pyy/Ptt, weighted by the fraction of each group in the population:

SP equals one when there is no differential clustering between group X and group Y and is greater than one when group X members live nearer to each other than they do to group Y members. In practice, SP can be converted to a zero-to-one scale by taking the quantity SP−1 (Massey and Denton 1988). White (1984) also has proposed a more complex standardization by taking f(dij)=dij2, which yields a statistic equivalent to the proportion of spatial variance explained.

Jakubs (1981) and Morgan (1983a, 1983b) have proposed that D and P* be adjusted to incorporate the effects of clustering. Massey and Denton

(1988) argue against this procedure because it confounds two different dimensions of segregation. They maintain that it is better to measure clustering directly as a separate dimension than to try to adjust other measures to reflect it.

The fourth dimension of segregation is centralization, or the degree to which a group is located near the center of an urban area. In the postwar period, African-Americans became increasingly isolated in older central cities as whites gravitated to the suburbs. Centralization is measured by an index that reflects the degree to which a group is spatially distributed close to or far away from the central business district (CBD). It compares a group’s distribution around the CBD to the distribution of land area around the CBD by using a formula adapted from Duncan (1957):

where the n areal units are ordered by increasing distance from the CBD and Xi and Ai are the respective cumulative proportions of group X members and land area in unit i.

In most circumstances, the centralization index varies between plus one and minus one, with positive values indicating a tendency for group X members to reside close to the city center and negative values indicating a tendency for them to live in outlying areas. A score of zero means that the group has a uniform distribution throughout the metropolitan area. The index states the proportion of group X members who would have to change their area of residence to achieve a uniform distribution around the CBD.

The last dimension of segregation is concentration, or the relative amount of physical space occupied by a minority group in the urban environment. Concentration is a relevant dimension of segregation because discrimination restricts minorities to a small set of neighborhoods that together account for a small share of the urban environment. The index of concentration takes the average amount of physical space occupied by group X relative to group Y and compares that quantity to the ratio that would obtain if group X were maximally concentrated and group Y were maximally dispersed:

where areal units are ordered by geographic size from smallest to largest, ai is the land area of unit i, and the two numbers n1 and n2 refer to different points in the rank ordering of areal units from smallest to largest: n1 is the rank of the unit where the cumulative total population of units equals the total minority population of the city, summing from the smallest unit up, and n2 is the rank of the areal unit where the cumulative total population of units equals the majority population, totaling from the largest unit down. T1 equals the total population of areal units from 1 to n1, and T2 equals the total population of areal units from n2 to n. As before, ti refers to the total population of unit i and X is the number of group X members in the city.

In most circumstances, the resulting index varies from minus one to plus one; a score of zero means that the two groups are equally concentrated in urban space, and a score of minus one means that group Y’s concentration exceeds group X’s to the maximum extent possible; a score of positive one means the converse. In certain circumstances, however, Egan et al. (1998) demonstrate that whenever the number of group X members is very small and the areas in which they live are very large, the index becomes unbounded in the negative direction. Thus, caution should be used in measuring the concentration of groups with very few members.

Which of these five indices of segregation is chosen for a particular application depends on the purpose of the study. All are valid measures, and arguments about which one is ‘‘correct’’ or ‘‘best’’ are meaningless, since they measure different facets of segregation. D provides an overall measure of evenness that is highly comparable with prior work, widely understood, readily interpretable, and independent of population composition. P* captures the degree of interand intragroup contact likely to be experienced by members of different groups and directly incorporates the effect of population composition. Most recent work has relied most heavily on these two segregation mea-

sures (Massey and Denton 1993; Frey and Farley 1994, 1996; Massey and Hajnal 1995; Peach 1998).

Neither D nor P* is inherently spatial, however, and each may be applied to study nongeographic forms of segregation, such as segregation between men and women across occupations (see Jacobs 1989). The remaining three dimensions are relevant whenever it is important to know about the physical location of a group in space. If the extent to which group members cluster is important, SP should be computed; if it is important to know how close to the city center a group has settled, CE may be calculated; and if the amount of physical space occupied by a group is relevant, CO is the appropriate index.

The most comprehensive understanding of residential segregation is achieved, however, when all five indices are examined simultaneously. That multidimensional approach yields a fuller picture of segregation than can be achieved by using any single index alone. Thus, Massey and Denton (1989) found that blacks in certain U.S. cities were highly segregated on all five dimensions simultaneously, a pattern they called ‘‘hypersegregation.’’ Denton (1994) has shown that this pattern not only persisted to 1990 but extended to other metropolitan areas. By relying primarily on the index of dissimilarity, prior work overlooked this unique aspect of black urban life and understated the severity of black segregation in U.S. cities.

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