Theil Segregation Index
Also known as: Theil's H, information theory index, entropy segregation index, multigroup entropy index
Theil's information index, denoted H, is an entropy-based measure of segregation that, unlike the two-group dissimilarity index, handles any number of groups at once. It compares the diversity (entropy) found within each unit to the diversity of the whole population: segregation is high when units are internally homogeneous even though the overall population is diverse. Its defining virtue is exact decomposability across nested levels and across groups.
Key highlights
- Handles any number of groups simultaneously, unlike the two-group dissimilarity index.
- Exactly decomposable across nested spatial or organizational levels (between vs. within).
- Decomposable across groups, isolating each group's contribution to total segregation.
- Grounded in information theory with a clear interpretation as the diversity explained by between-unit differences.
Intuition
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How it works
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When to use it
Use Theil's H when segregation involves more than two groups, when you need to decompose segregation across nested geographic levels (region, district, neighborhood) or organizational levels, or when you want each group's contribution to total segregation. It is the preferred multigroup evenness measure and the natural choice for analyzing how segregation is distributed across scales. It is less intuitive than the dissimilarity index's relocation interpretation, does not capture exposure or spatial clustering, and like other aspatial indices ignores the arrangement of units. Small units and sparse cells bias it upward unless a bias correction is applied.
Strengths & limitations
- Handles any number of groups simultaneously, unlike the two-group dissimilarity index.
- Exactly decomposable across nested spatial or organizational levels (between vs. within).
- Decomposable across groups, isolating each group's contribution to total segregation.
- Grounded in information theory with a clear interpretation as the diversity explained by between-unit differences.
- Lacks the simple 'share that must relocate' interpretation of the dissimilarity index.
- Measures evenness only — not exposure, clustering, or concentration.
- Aspatial: ignores the relative location of units.
- Biased upward with small units or sparse counts unless an explicit bias correction is used.
Common pitfalls
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Applications
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Frequently asked
Why use Theil's H instead of the dissimilarity index?
The dissimilarity index compares only two groups and cannot decompose segregation across levels. Theil's H handles any number of groups at once and, because entropy is additively decomposable, splits total segregation into between- and within-level components and into per-group contributions. When the setting is multigroup or multilevel, H provides analyses the dissimilarity index simply cannot.
What does an H value mean substantively?
H is the proportion of the population's total diversity (entropy) that is attributable to differences between units rather than within them. H = 0 means every unit has the same composition as the whole population (no segregation); H = 1 means every unit is internally homogeneous (complete segregation). It is a relative-diversity measure rather than a relocation count.
How does the decomposition property help?
Because H decomposes additively, you can ask how much of total segregation occurs between large units (e.g., school districts) versus within them (e.g., schools within districts), and how much each group contributes. This pinpoints the geographic scale and the groups driving segregation, guiding policy and theory in ways a single undecomposable number cannot.
Sources
- 1.Theil, H., & Finizza, A. J. (1971). A note on the measurement of racial integration of schools by means of informational concepts. Journal of Mathematical Sociology, 1(2), 187–193.
- 2.Reardon, S. F., & Firebaugh, G. (2002). Measures of multigroup segregation. Sociological Methodology, 32(1), 33–67.
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ScholarGate. (2026, June 22). Theil Segregation Index. ScholarGate. https://scholargate.app/sociology/theil-segregation-index