1. What should an index of segregation measure? Rebecca Allen (r.allen@ioe.ac.uk) Institute of Education, University of London Presentation to Bristol Segregation Workshop

2. Introduction Segregation means separation, stratification, sorting – Unevenness or dissimilarity – Isolation or exposure – spatial measures: concentration, clustering, centralisation Types and locations of segregation – Gender, race, income, social class – Schools, neighbourhoods, industries, workplaces How should we measure segregation? – Positive debates about measurement – does an index have good properties? – Normative debates about measurement – what properties of an index are appropriate to our research questions? Why measure segregation? – Descriptive statistics – Effects – segregation as one cause of inequalities – Causes – segregation as the outcome of a process

3. Segregation curve approach to measuring unevenness

4. Index of dissimilarity (D) ‘The proportion of one group that would have to re-locate to generate no segregation (holding the location of the other group constant)’ Relative index: 0 means no segregation 1 means complete segregation

5. Gini segregation index (G) Relative index: 0 means no segregation 1 means complete segregation

6. Hutchens segregation index (O) Relative index: 0 means no segregation 1 means complete segregation

7. Hutchens can place weights on different parts of the segregation curve Lambeth and Birmingham have same levels of segregation, according to D Birmingham has concentrations of advantaged schools Lambeth has concentrations of disadvantaged schools Hutchen’s indices will display a different value of segregation, depending on the chosen value of c

8. Properties of a ‘good’ unevenness segregation measure 1.Scale or composition invariance 2.Symmetry in groups 3.Movement between groups (principle of transfers) 4.Insensitivity to proportional divisions 5.Aggregative and additive decomposability 6.Symmetry in types 7.Range of 0-1

9. An alternative to the segregation curve approach S is an absolute index with meaning: ‘proportion of girls that would have to exchange schools in order to achieve evenness’ Not a segregation curve approach since it depends on the relative sizes of the two groups (girls and boys) Not a commonly used index, but used by Gorard et al. (2003 - school segregation); OECD (1980) for employment segregation; Krugman for industrial segregation

10. 10 girls arrive on a coach and are assigned on the same basis as existing girls GirlsBoysTotal School 1113041 School 2113041 School 3222042 School 4331043 School 5331043 110100210 D0.4 S0.19 GirlsBoysTotal School 1103040 School 2103040 School 320 40 School 4301040 School 5301040 100 200 D0.4 S0.2

11. 10 girls displace 10 boys in the schools (first version) GirlsBoysTotal School 1103040 School 2103040 School 320 40 School 4301040 School 5301040 100 200 D0.4 S0.2 GirlsBoysTotal School 1112738 School 2112738 School 3221840 School 433942 School 533942 11090200 D0.4 S0.18

12. 10 girls displace 10 boys in the schools (second version) GirlsBoysTotal School 1103040 School 2103040 School 320 40 School 4301040 School 5301040 100 200 D0.4 S0.2 GirlsBoysTotal School 1112940 School 2112940 School 3221840 School 433740 School 533740 11090200 D0.444 S0.2

13. The desirability of fixed upper and lower bounds S is not bounded by 0 and 1 The upper bound is 1-p, i.e. S can never display a value above 1-p Buckinghamshire: S = 0.48; p = 6%; max possible value of S = 0.94 Tower Hamlets: S = 0.11; p = 60%; max possible value of S = 0.40

14. Non-symmetry of the index makes interpretation of changes difficult The value of FSM segregation is not the same as the value of NONFSM segregation using S S is capable of showing that FSM segregation is rising and NONFSM segregation is falling simultaneously Poole 1999-2004: S FSM rose by 10%; S NONFSM fell by 27%

15. Does it matter which index is used? 1.The magnitude of the fall in segregation between 1989 and 1995 is 10% using S and 5% using D 2.S and D disagree on whether segregation actually fell or rose in an LEA between 1989 and 1995 in 35% of cases 3.If we placed LEAs in deciles according to their level of segregation, the 2 indices would disagree about which decile the LEA should be in 63% of the time

16. Index of Isolation (I) Measures the probability that random girl shares a unit with another girl Mean exposure of girls to other girls Relative index: Value of overall girls proportion means no segregation 1 means complete segregation May be low when the minority group is very small, even if it is very unevenly distributed Can be stretched (modified) onto a 0-1 bounded index, but no longer strictly reflects isolation/exposure

17. Further complexities in measuring segregation 1.Girls and boys in schools 2.Women in the labour market 3.Black, Hispanic, Asian children in schools 4.Poor (FSM) children in schools 5.Black families in neighbourhoods A segregation index changes because: 1.Assignment rule changes 2.Size of minority proportion changes 3.Size of units changes

18. Conclusions All methods of measuring segregation have: 1.an ‘index of segregation’ underlying them 2.a set of properties that describe how their measure will behave in particular circumstances 3.a set of normative principles that explain the suitability of the properties of their measure, given the research question

19. Discussion 1.To what extent are segregated schools in America responsible for the black-white test score gap? 2.What proportion of wage inequalities between men and women are due to workplace segregation? 3.To what extent have recent immigrants to Britain integrated with the White British population? 4.Why are schools in some parts of England more segregated than in other parts? 5.Does religious segregation in Northern Ireland reduce or increase criminal activity?