Isolation index

Isolation index measures the degree to which people inhabit geographic units inhabited primarily by members of their own group. It is usually denoted by I. It varies from 0 to 1.0 and is defined as the proportion of own-group members in the unit of the average person. In measuring black isolation, for example, a score of 1.0 means that the average black person lives in a neighborhood that is 100 percent black, and a score approaching 0 means that this person lives in a neighborhood where he or she is nearly the only black resident.[1] They have been used in studies of racial segregation[2] and ideological segregation.[3][4] Isolation index is not invariant to relative size of group.

Examples of isolation indices include Lieberson's isolation index and Bell's isolation index.[5]

Formula

The formula to compute the isolation index is given by:

${\displaystyle I=\sum _{i=1}^{n}[({\frac {a_{i}}{A}})({\frac {a_{i}}{a_{i}+b_{i}}})]}$

where ${\displaystyle a_{i}}$ is the population of group ${\displaystyle A}$ in region ${\displaystyle i}$, ${\displaystyle b_{i}}$ is the population of group ${\displaystyle B}$ in region ${\displaystyle i}$, ${\displaystyle A}$ is the total population of group ${\displaystyle A}$.

Numerical Example

Consider the following distribution of white and black population across neighborhoods.

Neighborhood	White	Black	${\displaystyle I_{i}}$
A	100	5	0.01
B	100	10	0.036
C	100	10	0.036
Total	300	25	0.082

References

1. Massey, Douglas S.; Denton, Nancy A. (December 1988). "The Dimensions of Residential Segregation". Social Forces. 67 (2): 281. doi:10.2307/2579183. ISSN 0037-7732. JSTOR 2579183.
2. "SexRacial Residential Segregation Measurement Project". Population Studies Center, University of Michigan. Archived from the original on 2011-05-17. Retrieved 2010-12-06.
3. Chadwick Matlin; Jeremy Singer-Vine; Chris Wilson (April 29, 2010). "Escape From the Echo Chamber". Slate magazine.
4. Matthew Gentzkow; Jesse M. Shapiro (3 November 2011). "Ideological Segregation Online and Offline". Quarterly Journal of Economics. 126 (4): 1799–1839. doi:10.1093/qje/qjr044. hdl:1811/52901.
5. Robinson, V. (1980). "Lieberson's Isolation Index; A Case Study Evaluation". Area. 12 (4): 307–312. JSTOR 20001630.

See also

• Diversity index
• Index of dissimilarity