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«reNtal HousiNg Policy iN tHe uNited states Volume 13, Number 2 • 2011 U.S. Department of Housing and Urban Development | Office of Policy ...»

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This article demonstrates an alternative approach that accounts for local-level segregation below the city and county level that minimizes the effects of MAUP. This approach shifts the context of the analysis from a solely segregation standpoint to one that also exhibits integration among racial or ethnic groups. This approach recasts regional patterns of segregation in a way that highlights other regional problems associated with the pervasive problems resulting from the concentration of minorities. This article is the first of two that examine segregation at the regional level.

The data used for this analysis are from the American Community Survey (ACS) 5-year estimates from 2005 to 2009 by the U.S. Census Bureau. Percentages and measures are derived to reveal changing patterns of segregation and integration from the factoring of local variation into the analysis. This analysis will identify not just succinct jurisdictions (cities and counties) of segregation but large areas (clusters of contiguous jurisdictions) that form subregions. The focus of this analysis is between the White and Black populations in the contiguous United States.

The United States has a long history of regional segregation between the Black and White populations. The Black population constitutes 13 percent of the total population with most living in 19 percent of the cities and counties across the United States. Translated into geography, the Black population primarily resides in only 9 percent of the entire country. A look at the geographic distribution of those percentages shows a very clear pattern of regional segregation (see exhibit 1).2 For a thorough discussion of MAUP, see Openshaw (1994).

See the appendix for corresponding frequency distributions for all maps.

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The concentration of the Black population appears to form a solid belt of cities and counties from east Texas straight across the southern states and continuing up the east side of the Carolinas, ending mainly around Baltimore, Maryland. Also, several small and loosely coupled regions of Black concentrations are in the northeastern, midwestern, and western states. The north-central states are relatively devoid of the Black population.

Several problems emerge when examining segregation this way. First, this map displays only the results of one value and has no larger comparative context. The percentage is a comparative measure, only in a relative sense, as a proportion and the resulting map leaves an assumption about the distribution of the White population. It can be assumed that the White population lives in areas where there are low percentages of Blacks or the two populations are more balanced where the percentages are moderate, but this cannot be ascertained without actual values incorporated into the analysis. Second, when one group of the population is unevenly distributed across an area, a thematic mapping classification scheme must be selected that allows patterns in the data to be distinguished. In this instance, the quantile classification scheme is used because of a significant amount of variation in the frequency distribution. This scheme3 nicely highlights clusters of like The quantile classification groups equal numbers of jurisdictions into each data partition.

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values but includes too wide of a range of values in the highest partition; the range of data values in this partition is exaggerated when the distribution is highly skewed. A look at the legend shows that 16 to 87 percent of the Black population is contained within that belt. A geographic pattern forms that includes many jurisdictions that do not have similar percentages. This geographic pattern is exaggerated with respect to the size of the regional concentration of the Black population, and using any of the other classification schemes does not offer a solution. The other schemes either hide patterns or create inappropriate data partitions on skewed frequency distributions. As a result of these problems, percentage maps do not communicate the message about segregation as precisely as they should; they should depict the true geographic extents and patterns of regional segregation.

The final problem, though, is that city and county population counts are straight summations of lower level tallies in which variation from the lower geographies is erased by the MAUP. This summation can significantly affect the display of geographic patterns, regardless of the thematic mapping classification scheme used.

The way to get a first indication of hidden levels of segregation within a jurisdiction is through mapping local variation of percentage point differences between the White and Black populations.

Variation is measured as the standard deviation of the absolute differences between the percent of the White and Black population across the underlying census tracts for each jurisdiction (see exhibit 2).

Exhibit 2 Variation of White and Black Population Percentage Differences Within Cities and Counties––Quantile Classification

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The resulting data frequency distribution again requires the quantile thematic mapping classification scheme to map the data. A low standard deviation will indicate a more even distribution of each racial group across the jurisdiction because of little variation in the percentage point differences from the tracts within the jurisdiction. Conversely, a high standard deviation signifies a large variation in percentage point differences between the underlying tracts. It cannot be discerned whether or not the percentage point differences are small or large, because this method reveals only whether a variation exists across tracts within a jurisdiction.





There is a significant change in the geographic patterns compared with the single percentage map of the Black population in exhibit 1. The belt across the southern states and into the northeastern states is still present, but the pattern has become diluted, revealing a more dispersed level of regional segregation. What is revealed, however, is that many of the jurisdictions within the belt have similar percentages of the White population, indicating a more integrated population. A large regional cluster of high variation between the two groups is now present in the four-corner states of Arizona, Colorado, New Mexico, and Utah. Several small clusters of high variation between groups also now appear in the north-central states. Finally, several jurisdictions in the northeastern states have high variations in the differences between the two groups, indicating they are more segregated than shown in the single percentage map. These pattern changes hint that segregation is a localized phenomenon that varies significantly.

Although the map in exhibit 2 compares one population with another, it still does not situate either group in the context of the combined populations to determine how segregated the two groups are within a jurisdiction. Using this map makes it difficult to discern which racial group is dominant across a region, but historical knowledge of segregation in the United States, in general, is a good indicator. Nevertheless, the advantage of using this map is that it gives an indication of the differences between the White and Black populations that may prompt an examination of jurisdictions that are more segregated than others at the local level. Further, the skewed shape of the distribution continues to prevent the use of a thematic map classification scheme that can equalize the class partitions. The use of a diversity index can help alleviate these continuing problems by transforming the data into a form that addresses the previous technical and substantive issues.

Several dissimilarity and diversity index measures can be applied to data to depict levels of segregation.4 In this analysis, Theil’s entropy index5 is used because it has mathematical properties that are sensitive to disproportionality changes between two or more groups that matches the theoretical aspects of changes in segregation levels in place. The resulting index allows for an examination of segregation between the two groups in comparison to the total population between them (see exhibit 3).6 More importantly, with the re-expression of data, the equal interval classification scheme can be used, because the variation across the full range of values has been reduced and standardized.

This scheme partitions data values into equal ranges and is not affected by the distribution of the data. This grouping makes the ranges comparable with each other and, subsequently, affects the map by limiting the geographies in the highest partition to those that are truly different with respect to what is being analyzed, which, in this case, is the levels of segregation of the Black population.

For a full analysis of several common indexes, see Reardon and Firebaugh (2002).

For the mathematical details of Theil’s entropy index, see the appendix.

Values closer to 0 indicate more segregation and values closer to 1 indicate more integration.

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The map in exhibit 3 has three distinct advantages over the original percentage map in exhibit 1.

The first advantage is a more succinct regional segregation pattern. The index has produced values that express the magnitude of difference between the two groups based on how integrated each group is in comparison with the total population of each other. The regional belt of Black population concentration from east Texas to northern Maryland is still prevalent but has been thinned out and slightly broken up. The concentration of the Black population is now in 14 percent of the jurisdictions across the United States, a reduction of 5 percentage points from the percentage map in exhibit 1. The index, however, detects levels of segregation only between two groups and does not indicate which group dominates on either end of the range. Again, a historical knowledge of the distribution of racial groups in the United States will indicate which group is more dominant in a particular region. The second advantage is that the map more accurately shows where the two groups are segregated and integrated. Many jurisdictions have indexes that are in the upper partitions of the distribution with several states in the belt showing a significant level of integration between Whites and Blacks. With this map, Florida is much more distinguishable as being segregated within the state because the index values show greater variation. Third, the remainder of the jurisdictions across the United States continues to be widely distributed, but the indexes are now in the lowest partition compared with the percentage map in exhibit 1. The exception is California, in which several jurisdictions have indexes in the middle partitions indicating a greater level of statewide segregation.

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An interesting result is that the cities of Chicago, Detroit, St. Louis, and Indianapolis show up in the highest partition, indicating a high level of integration between the two populations, although it is well known that they are very segregated cities. The previous results are still subjugated to MAUP, because the data used at the city and county levels demonstrate a loss of information because the population counts used are summed from the underlying geography. This same effect is also likely occurring in many other jurisdictions; this likelihood is of concern. To compensate for this effect, the diversity index can be adjusted for the underlying local segregation between the two racial groups across the census tracts contained within a jurisdiction.6 (See exhibit 4.) The main observation in exhibit 4 is that the belt that stretches across the southern states and up the east coast has thinned out more and broken apart, forming small regions of integration with a coherent pattern of regional segregation. This map is more accurate because the two populations have been placed in context with each other and local levels of segregation have been factored in. The concentration of the Black population in exhibit 4 is now in 8 percent of the jurisdictions across the United States. Two specific examples exemplify the corrective adjustment the localized index makes. In exhibit 3, Chicago, Detroit, Indianapolis, and St. Louis each has an index in the highest class, which indicates that it is very integrated between the two populations. The adjustment Exhibit 4 Localized Diversity Levels of Cities and Counties—Equal Interval Classification

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for local variation minimizes the effect of the MAUP and shifts the index to a level that is more reflective of the segregation in the underlying geography. A similar instance is in Bibb County, Alabama, which is located south of the city of Birmingham in the center of the state. This jurisdiction is now an island of high segregation within a region of high integration in the surrounding jurisdictions. The city of Birmingham, which is just northeast of Bibb County, was also reduced from the highest partition to the middle and now matches the surrounding counties, all of which remained in the same partition after the adjustment. The two jurisdictions now stand in stark contrast to each other. The variation across the rest of the United States is further attenuated, indicating a more realistic portrait of much of the county having little in the way of a Black population. In addition, the original percentage map in exhibit 1 showed that nearly all jurisdictions in Mississippi were in the highest partition of the Black population. Mississippi now has clear interior geographic patterns of segregation and integration. The geographic patterns in the underlying variation in exhibit 2 also revealed this trend, but the effects of the quantile thematic mapping scheme made it unclear whether the changes resulted from a wide range of high and low values being partitioned together. Also, the racial groups in exhibit 2 were not within the context of their combined populations. California still maintains several jurisdictions with indexes in the middle partitions with little adjustment for levels of segregation previously.



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