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

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

Segregation curve approach to measuring unevenness

Index of dissimilarity (D)

units

units area

unit

area

unit

shareboyssharegirlsD

BOYS

boys

GIRLS

girlsD

2

1

2

1

‘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

Gini segregation index (G)

PPN

girlspropgirlsprop

G

N

i

N

jnjni

12 2

1 1

Relative index:•0 means no segregation•1 means complete segregation

Hutchens segregation index (O)

Relative index:•0 means no segregation•1 means complete segregation

i

c

i

iic shareboys

sharegirlsshareboysxO 1)(

Hutchens can place weights on different parts of the segregation curve

Figure 10: Segregation Curves for Lambeth and Birmingham

0.2

.4.6

.81

Cum

ulat

ive

shar

e of

FSM

pup

ils

0 .2 .4 .6 .8 1Cumulative share of NONFSM pupils

Lambeth D=0.38 (2004)

Birmingham D=0.38 (2004)Line of equality

• 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

Properties of a ‘good’ unevenness segregation measure

1. Scale or composition invariance2. Symmetry in groups3. Movement between groups (principle of

transfers)4. Insensitivity to proportional divisions5. Aggregative and additive decomposability6. Symmetry in types7. Range of 0-1

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

)1(**5.0 propgirlsDsharetotalsharegirlsSi

ii

i

shareboyssharegirlsD *5.0

10 girls arrive on a coach and are assigned on the same basis as existing girls

  Girls Boys Total

School 1 11 30 41

School 2 11 30 41

School 3 22 20 42

School 4 33 10 43

School 5 33 10 43

  110 100 210

D 0.4

S 0.19

  Girls Boys Total

School 1 10 30 40

School 2 10 30 40

School 3 20 20 40

School 4 30 10 40

School 5 30 10 40

  100 100 200

D 0.4

S 0.2

10 girls displace 10 boys in the schools (first version)

  Girls Boys Total

School 1 10 30 40

School 2 10 30 40

School 3 20 20 40

School 4 30 10 40

School 5 30 10 40

  100 100 200

D 0.4

S 0.2

  Girls Boys Total

School 1 11 27 38

School 2 11 27 38

School 3 22 18 40

School 4 33 9 42

School 5 33 9 42

  110 90 200

D 0.4

S 0.18

10 girls displace 10 boys in the schools (second version)

  Girls Boys Total

School 1 10 30 40

School 2 10 30 40

School 3 20 20 40

School 4 30 10 40

School 5 30 10 40

  100 100 200

D 0.4

S 0.2

  Girls Boys Total

School 1 11 29 40

School 2 11 29 40

School 3 22 18 40

School 4 33 7 40

School 5 33 7 40

  110 90 200

D 0.444

S 0.2

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

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: SFSM rose by 10%; SNONFSM fell by 27%

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

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

i units

propgirlssharegirlsn

girls

GIRLS

girlsI .

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 changes2. Size of minority proportion

changes3. Size of units changes

Conclusions

All methods of measuring segregation have:1. an ‘index of segregation’ underlying them2. a set of properties that describe how their

measure will behave in particular circumstances3. a set of normative principles that explain the

suitability of the properties of their measure, given the research question

Discussion1. 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?