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