What should an index of school segregation measure?

Abstract

The paper aims to make a methodological contribution to the education segregation literature, providing a critique of previous measures of segregation used in the literature, as well as suggesting an alternative approach to measuring school segregation. It also provides new empirical evidence on changes in the extent of socio-economic segregation (measured by free school meals (FSM) entitlement) in English schools during the last fifteen years. Specifically, the paper examines Gorard et al.'s (2000aGorard et al.'s ( , 2003 finding that FSM segregation between schools fell significantly in the years following the 1988 Education Reform Act. Using Annual Schools Census data from 1989 to 2004, the paper challenges the magnitude of their findings, suggesting that the method used by Gorard et al. actually overstates the size of the fall in segregation by 100%. Our results show evidence of an increase in the index of dissimilarity in many Local Authorities, especially in London, although in the South-East as a whole we note that it falls. We also observe higher segregation in LEAs with higher proportions of pupils at voluntary-aided schools. We cannot confirm however, whether this is a causal relationship. It is not necessarily the case that the rise in the segregation index in these Local Authorities is attributable to the behaviour of VA schools. Much of this paper is a critique of previous methods used to measure segregation in schools. For example, we suggest that the GS index is not the optimal way of measuring changes in school segregation for the following reasons:1. GS is not bounded by 0 and 1: the upper boundary varies according to FSM eligibility, so GS is better described as an 'indicator' rather than an index of segregation; 2. GS is not symmetric, meaning that it is capable of showing that FSM segregation is rising and NONFSM segregation is falling simultaneously; and 3. GS is actually systematically variant to changes in overall FSM eligibility, except in the most stringent and unlikely of circumstances (the strict proportionate change in FSM); therefore we can properly describe it as composition variant. It had a tendency to fall as FSM eligibility rises, regardless of the change in the unevenness of school's shares of FSM and NONFSM pupils.In this paper we make the case for a segregation curve approach to measuring segregation and use one exemplar index, the index of Dissimilarity, to re-evaluate the extent of school segregation in England over the last fifteen years. What can we conclude?• There was no pervasive increase in segregation over the period.• There are a number of potential explanations for this. For example, it may be that de facto school choice did not in fact increase during this period due to capacity constraints.• The analysis does however provide clear evidence of an increase in segregation, as measured by the index of dissimilarity, in many Local Authorities, particularly in London. The index is also higher in LEAs with higher proportions of pupils educated at voluntary-aided schools...

Parental choice, neighbourhood segregation or cream skimming? An analysis of school segregation after a generalized choice reform

“…However, it does not fulfil all the desired properties of a segregation index (see Hutchens 2004 andAllen andVignoles 2007, for discussions). In particular, it does not fulfil the property of scale invariance, which implies invariance to relative changes in group proportions.…”

How Spatial Segregation Changes over Time: Sorting Out the Sorting Processes

“…While the Index of Dissimilarity always runs from 0 to 1, the Index of Segregation has an upper limit determined by the size of the group, x. If p x is the proportion of x in the total population (X/T), then the upper limit of S x is (1-p) (Allen and Vignoles 2007). This implies that one needs to be extremely careful when using the Index of Segregation to make comparisons over time as the meaning of a particular value of S x is dependent on the share of x in the overall population (Allen and Vignoles 2007).…”

“…Even within this dimension, there has been an intense debate over the most appropriate (Duncan and Duncan, 1955) An alternative is the Index of Segregation, S x , which measures the evenness of the distribution of group x with respect to the whole population, (t i and T), where Allen and Vignoles, 2007) The Index of Dissimilarity is preferred to the Index of Segregation (which was used by Dorling and Rees 2003, for example) because it is unaffected by the size of the group being considered. While the Index of Dissimilarity always runs from 0 to 1, the Index of Segregation has an upper limit determined by the size of the group, x.…”

Commentary

“…Allen and Vignoles (2007) argue that the index of dissimilarity (ID) exhibits the desirable properties of scale interpretability, size invariance, symmetry across groups and schools, school equivalence (SE), and the principle of transfers. Except for scale interpretability (see below), these properties are appropriate, but insufficient to underpin an index designed to track changes in school segregation through time, due to the impact of changing overall shares of (N)FSM pupils and changing total enrolments across schools.…”

“…Debate continues about the measurement of segregation, with recent contributions from Allen and Vignoles (2007); Cheng and Gorard (2010), Gorard (2007;2009;, and Johnston and Jones (2010; about the choice of an aspatial index and Harris and Johnston (2008), Harris (2011;2012), and earlier work by Gibson and Asthana (2000) who assess spatial measures.…”