What should an index of segregation measure?

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What should an index of segregation measure?

• Rebecca Allen (r.allen_at_ioe.ac.uk)
• Institute of Education, University of London
• Presentation to Bristol Segregation Workshop

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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

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Segregation curve approach to measuring unevenness
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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

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Gini segregation index (G)

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

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Hutchens segregation index (O)

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

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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
• Hutchens indices will display a different value
  of segregation, depending on the chosen value of c

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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

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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

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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
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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
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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
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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

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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

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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

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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

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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
• Assignment rule changes
• Size of minority proportion changes
• Size of units changes

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Conclusions

• All methods of measuring segregation have
• an index of segregation underlying them
• a set of properties that describe how their
  measure will behave in particular circumstances
• a set of normative principles that explain the
  suitability of the properties of their measure,
  given the research question

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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?