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]
The formula to compute the isolation index is given by:
I=
| n | ||
| \sum | [( | |
| i=1 |
| ai | )( | |
| A |
| ai | |
| ai+bi |
)]
where
ai
A
i
bi
B
i
A
A
Consider the following distribution of white and black population across neighborhoods.
| A | 100 | 5 | 0.01 | |
| B | 100 | 10 | 0.036 | |
| C | 100 | 10 | 0.036 | |
| Total | 300 | 25 | 0.082 |