Philip J. Ethington

Associate Professor of History

University of Southern California

213-740-1669

philipje@usc.edu

Segregation Indices[1]

Derived From: “Segregated Diversity” Report, July 2000:
http://www.usc.edu/dept/LAS/history/historylab/Haynes_FR/index.html

(1)“H” Entropy (or Diversity) Index

	K
H=	-Σ	Pk	Log Pk
	k=1

Where:

N=total population size

N_{k =}number of persons in Kth group

P_{k =} N_k /N

(2)Isolation and Interaction Index[2]

Isolation:

	n
xP*x=	Σ	[xi/X][xi/ti]
	i=1

Interaction:

	n
xP*y=	Σ	[xi/X][yi/ti]
	i=1

Where:

x_i = number of X members in the areal subunit i

y_i = number of Y members in the areal subunit i

t_i = Total population of number of the areal subunit i

X =Number of X members county-wide

(3) Index of Dissimilarity

	n
D=	Σ	[ti / |pI-P|/2TP(1-P)]
	i=1

Where:

t_i = Total population of areal subunit i

p_i = “minority” population of areal subunit i

T = Total population of whole county

P = “minority” population of whole county, which is subdivided into n areal units.

(4) Index of Relative Clustering (RCL)[3]

"This index is a measure of relative clustering, since it compares the average distance between X members (the minority) and Y members (the majority). It equals 0 when minority members display the same amount of clustering as the majority, and is positive whenever minority members display greater clustering than is typical of the majority. If minority members were less clustered than the majority, then the index would be negative. While simple to compute and interpret, this index has the disadvantage of having no theoretical maximum or minimum." (Massey and Denton 1988, pp 295-6).

RCL= P_xx/P_yy-1

Where " P_xx " and " P_yy " are first calculated as the

"Index of Spatial Proximity," as follows:

	n	n
Pxx =	Σ	Σ	xi xj cij /X^2
	i=1	j=1

…wherein:

xi	= the number of members of X group (Black, Hispanic, White, Other) of tract i
t j	= the total population of tract j
X	= the number members of X group (Black, Hispanic, White, Other) county wide
cij	= the negative exponential of the distance between the centroids of tract i and j.
n	= the number of census tracts (here, 1656)

(5) Relative Centralization[4]

	n		n
RCE =	(Σ Xi-1Yi)	-	(Σ X iY i-1)
	i=1		i=1

"…Where the n areal units are ordered by increasing distance from the central business district, and Xi and Yi are the respective cumulative proportions of X's and Y's population in tract i. This index varies between -1.0 and +1.0, with positive values indicating that X members are located closer to the city center than are members of GroupY, and negative values indicating that group X members are distributed farther form the city center. When the index is 0, the two groups have the same spatial distribution around the central business district. The index may be interpreted as the relative share of group X members that would have to change their area of residence to match the degree of centralization of Y members." (Massey and Denton 1988: 292)

Selected Citations Regarding Segregation Indices

Lieberson, Stanley 1981 “An Asymmetrical Approach to Segregation,” in Ethnic Segregation in Cities, edited by Ceri Peach, Vaughn Robinson an Susan Smith (Athens, GA: The University of Georgia Press, 1981): 61-82.

Massey, Douglas S. and Denton, Nancy A. “The Dimensions of Residential Segregation,” Social Forces 67:2 (December 1988): 281-315.

White, Michael J. "The Measurement of Spatial Segregation," American Journal of Sociology 88:5 (March 1983): 1008-1018.

White, Michael J. “Segregation and Diversity Measures in Population Distribution,”

Population Index. 52 (1986): 198-221.

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[1] See White 1986; Massey and Denton

1988

[2] See especially Lieberson 1981

[3] See Massey and Denton (1988); White (1986).

[4] See Massey and Denton 1988