Segregation is a spatial outcome of spatial processes that needs to be measured spatially and at a scale meaningful to the study. This is the axiom from which local indices of segregation are developed and applied to the patterns of admission observed for cohorts of pupils entering London's state-funded secondary (high) schools in each of the years from 2003 to 2008. The indices - local indices of difference, isolation and of concentration – are used to measure social segregation not between arbitrary areas or regions but specifically for schools that overlap in regard to their admission spaces. This is made possible by the use of detailed and geographically referenced governmental micro-data that allow the pupil flows from elementary to high schools to be modeled and therefore "competing" schools to be identified. Using eligibility for free school meals as a measure of social segregation, sizable differences in the proportions of FSM eligible pupils recruited by apparently competing schools are found, with selective schools especially and also faith schools under-recruiting such pupils. Whilst there is some evidence that social segregation has decreased over the period, the trend is considered to be an artifact of using free school meals as a measure of disadvantage. As such the problem shifts from at what scale to measure between-school segregation to what actually is an appropriate measure to use.

1. Using geographical micro-data to measure
segregation at the scale of competing
schools in London
Richard Harris
School of Geographical Sciences &
Centre for Market and Public Organisation
University of Bristol, UK

2. Outline
There is an argument that “school choice” (in the UK)
leads to social segregation.
Segregation is a spatial outcome of spatial processes that
are spatially variable.
Aim, therefore is to develop local indices of segregation
developed and applied, not between arbitrary areas or
regions but specifically for schools that overlap in regard
to their admission spaces.

3. Outline
Use detailed and geographically referenced
governmental micro-data (PLASC/NPD) that allow pupil
flows from primary (elementary) to secondary (high)
schools to be modelled, therefore "competing" schools
to be identified.
Looking to see if there is a separation of more and less
economically (dis-) advantaged pupils as they make the
transition from primary to secondary schools.
Which would suggest a process of social sorting over-
and-above prior sorting (by neighbourhood geography
and by primary school).

4. Context
Study region is Greater London, with 382 516 records of
pupils who entered one of 384 state-funded secondary
schools in any one of the years 2003 to 2008.
It has been reported that only one quarter of pupils in
London go to their nearest secondary school (Burgess et
al 2008)
… who also find that there is an average of 37 feeder
primary schools per secondary school in London.
Which implies a ‘noisy system’

5. Showing the typical number of feeder primary schools
a secondary school in London has for
a certain percentage of its intake in 2008

6. But… it is easy to exaggerate…

7. Showing the links between primary and secondary schools
for the first 50% of the intake into each secondary school
(shown for a part of London in 2008).
Evidence of
geographical
clustering?
 Cf. Hamnett and
Butler 2011
’Geography
Matters’: the role
distance plays in
reproducing
educational
inequality in East
London TIBG 36
479–500

8. The geography…
… is not surprising
It isn’t a choice system
When demand for places exceeds supply, admissions
criteria are used and these often make allocations based
on where the pupil lives (in general, proximity to the
school).
Schools that select by faith or by entrance exam are the
exceptions.
Pupils still tend to go to a local school.

9. Consequently…
Schools that recruit a
higher proportion of
FSM eligible pupils
tends to be competing
with schools that do the
same.
Reflects neighbourhood
geographies.
But are there local
differences between
competing schools?

10. How to define “competing”?
The graph shows secondary schools
that are connected by one or more
primary school.
The level of ‘competition’ between
schools is quantified in the form of a
weights matrix
 the weight between any two competing
schools (iand j) is the (joint) probability
that a pupil selected at random from
secondary school i attended the same
primary school as a pupil selected at
random from secondary school j.
 The weights are then scaled (row-
standardised) so that the sum of the
weights for any school is equal to one.

11. From the weights matrix to the local indices of
segregation
A local and spatial index of segregation is here defined as
one where
 (a) each zone or place in the study region is considered
with respect to all others with which it interacts, is
proximate to, shares a border and/or with which there is
an interdependency or connection; and
 (b) where a separate index value is calculated for every
zone or place within the study region (as opposed to
having one summary average for them all) so their
distribution of the values across the study region can be
considered

12. Three measures
Local index of difference (of dissimilarity)
 Where p is the proportion of FSM eligible pupils
Local index of isolation
Local index of clustering
Their share characteristic is the (spatial) weights matrix

13. Index values for 2008
by school type

14. LID scores (2008)

15. So, local differences but are they getting worse
(or better)?
(no!)

16. Conclusions
The substantive conclusion of the case study is that
apparently competing secondary schools do not recruit
equal proportions of FSM eligible pupils.
 Smithers& Robinson (2010) find that comprehensive
schools in England are highly socially segregated
Across London, in 2008, the mean difference between a
school and its average competitor was 0.078 (7.8
percentage points) against an overall proportion of 0.268
of pupils eligible for FSM.

17. Conclusions
The patterns of segregation vary geographically and by
school type, with schools that select either by faith or by
academic ability tending to under recruit FSM eligible
pupils relative to their competitors.
Whilst there is no evidence that the social segregation
has increased over the period 2002 to 2008, the evidence
it may have decreased is rendered uncertain by the
underlying inconsistency of what FSM eligibility
measures at any time period.

18. Conclusions
However, some stability is not especially surprising when
it isn’t a school choice system at all, only the right to
express a preference.
It is likely that these admissions criteria create and
maintain differences between schools (in regard to who
they are recruiting) but what should the policy response
be?
 Lottery for places? Guarantee right of entry to a particular
choice set of schools?

19. References
Harris, RJ, 2011, Measuring segregation – ‘a geographical tale',
Environment and Planning A, 43, pp. 1747-1753.
Harris RJ, 2012, Local indices of segregation with application
to social segregation between London’s secondary schools,
2003 – 2008/9, Environment and Planning A, in press.
Harris RJ, 2012/13, Geographies of transition and the
separation of lower and higher attaining pupils in the move
from primary to secondary school in London, Transactions of
the Institute of British Geographers, in press.