What should an index of school segregation measure?

Abstract The article 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 segregation. Specifically, the paper examines Gorard, Fitz and Taylor's finding that social segregation between schools, as measured by free school meals (FSM) entitlement, 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. seriously overstates the size of the fall in segregation. We make the case for a segregation curve approach to measuring segregation, where comparisons of the level of segregation are possible regardless of the percentage FSM eligibility. Using this approach, we develop a new method for describing both the level and the location of school segregation. Acknowledgements The authors would like to thank Simon Burgess, Steve Gibbons, Harvey Goldstein, Graham Hobbs, Stephen Jenkins, Rosalind Levačić, Philip Noden, John Micklewright and Andrew Ray for their comments. Also thanks to the Economic and Social Research Council and the Department for Education and Skills for financial assistance. Notes 1. The other dimensions being exposure (isolation), concentration (the amount of physical space occupied by the minority group), clustering (the extent to which minority neighbourhoods abut one another), and centralisation (proximity to the centre of the city). 2. These five principles relate to Hutchen's axioms 1, 2, 3, 4 and 7. Axioms 5 and 6 relate to an ability to aggregate and additively decompose a segregation index; D does not satisfy these axioms. 3. We define an upper limit as being the value of an index when each school either has only FSM pupils or only NONFSM pupils; and never has a mixture of the two. We recognise that it is not always technically possible to achieve this in many cases. 4. Note that 2*p(1‐p) is the maximum possible value of the weighted sum of the absolute deviations of the FSM proportion for each school: , where pi is the FSM percentage in school i. 5. In practical terms this actually means that a large constant proportionate increase in FSM is often not achievable because the most deprived school does not have enough NONFSM pupils to lose. 6. The segregation curve approach is not the only way to demonstrate the independence of the value of D to changes in p: Zoloth (Citation1976) gives a short mathematical decomposition of D's formula to show the same result. 7. Using FSM take‐up, GS is 0.353 in 1991; 0.329 in 1992; 0.308 in 1993; 0.298 in 1994; 0.300 in 1995. 8. Though we do not discuss it in this article, we recognise that D should only be cautiously used as a dependent variable in a regression for two reasons. First, its use as a dependent variable means that we treat the values of the index as having cardinal meaning, so we would only want to do this where we accepted the linear payoff criterion of D as being appropriate given our view of segregation and social welfare. Second, we recognise that D displays a systematic random allocation bias where the value is non‐zero even under random allocation and the extent of the bias depends on various features of each LEA.