Example of a Composite Measure

Using the “Index of Dissimilarity” to Measure Residential Racial Segregation

By Steven W. Peuquet, Ph.D.

Center for Community Research & Service, University of Delaware

Definition

The “index of dissimilarity” (D) is the most commonly used and accepted method of measuring segregation, and compares how evenly one population sub-group is spread out geographically compared to another population sub-group. The sub-groups analyzed can be defined in a variety of ways, including race (e.g., blacks compared to whites), ethnicity (e.g., Hispanics compared to non-Hispanics) or income (e.g., people in poverty compared to those not in poverty).

Calculation

The Index of Dissimilarity is calculated mathematically as follows:

D = 100*0.5 *S | Pxi/Px - Pyi/Py|

Where:

D  =   the index of dissimilarity for two groups being compared within a specific

geographic area

Pxi =   the population of group x in census tract i

Px  =   the total population of group x in the overall geographic area

Pyi  =   the population of group y in census tract i

Py   =   the total population of group y in the overall geographic area

S  =   the Greek letter “sigma” indicating the summation of terms

Interpretation

The index equals 0.0, indicating complete integration of the two sub-groups, when all census tracts within the geographic area being analyzed have the same proportion of population sub-group members as in the whole geographic area. The opposite extreme is when the index equals 100.0, indicating complete segregation. In this extreme case, a few census tracts consist entirely of members of one population sub-group, while all the others contain all the members of the other population sub-group.  Another, perhaps easier way to interpret the value of the index is that it indicates the percentage of either sub-group (e.g., blacks or whites) who would have to move to another census tract in order for both sub-groups to be distributed evenly so as to achieve complete integration.  In a totally segregated environment (D = 100.0), 100% of either sub-group would have to move to achieve complete integration. Index values between 0.0 and 30.0 indicate low segregation, values between 31.0 and 60.0 indicate moderate segregation, and values between 61.0 and 100.0 indicate a high level of segregation (Massey and Denton, 1993, p. 20) (Exhibit IV-1).

Sources: Massey and Denton, 1993, p. 20; University of Delaware

Applying the Index to New Castle County, Delaware

In our analysis of African Americans (blacks) and Caucasians (whites), the results show that the index has been dropping consistently over this 30-year period for the county as a whole.  The index stood at 73.6 in 1970, 64.0 in 1980, 56.2 in 1990, and continued to fall to 50.8 in 2000 (Exhibit IV-7). This means that in the year 2000, 51% of blacks would have had to move from their present census tract to other tracts for the county to have become totally unsegregated.

When the city of Wilmington is analyzed separately, a positive, albeit minor improvement is apparent.  The City’s index value stood at 60.4 in 1970, then fell slightly to 59.7 and 59.6 for 1980 and 1990 respectively.  By the end of the 20th century the index stood at 56.5, only a minor downward change from where it was 30 years earlier in 1970 (Exhibit IV-7).

Overall, while the downward trend in the level of the black/white index of dissimilarity is encouraging, index values of 51.8 and 56.5 for New Castle County and Wilmington respectively for the year 2000 are within the upper part of the range which Massey and Denton define as “moderately segregated.”

The index of dissimilarity was also calculated for Hispanics and non-Hispanics for the years 1990 and 2000.  This index for the overall county stood at 35.8 in 1990 and increased slightly to 36.4 in 2000. For Wilmington the index dropped slightly from 48.5 to 45.5 over this 10-year period (Exhibit IV-8).  Like national findings, the results in New Castle County show that as the size of the Hispanic population continues to grow, it is not nearly as segregated as the African American population, and the degree of its segregation has changed little over the recent past.

Sources: University of Delaware; U.S. Census Bureau

Sources: University of Delaware; U.S. Census Bureau