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Abstract
This paper presents a new analysis of segregation between schools in terms of pupils living in poverty, for all secondary schools in England from 1996 to 2005. This shows that the clustering of similar pupils in specific schools increased noticeably from 1996 to 2001, but then settled at a level still below that of 1989 when official records began. The analysis uses four estimates of segregation using figures for take‐up of, and eligibility for, free school meals compiled to create both the dissimilarity index and what has been termed the Gorard index of segregation. All four estimates give the same substantive results and the findings for the dissimilarity index and the Gorard index of segregation using either measure of free school meals are indistinguishable. The two indices are, therefore, measuring the same thing. However, the Gorard index of segregation is again shown to be more tolerant of the precise measure being used and so more strongly composition invariant than the dissimilarity index. This has important implications both for the past debate on how to measure segregation between schools and for how education authorities go about estimating segregation in the future.
Notes
1. The Gorard (Citation1997) paper and what followed was something of a breakthrough, both in terms of the methods and data used to examine the impact of school choice and in the results that ran contrary to almost all of the UK work that had gone before it—as any citation search will attest. That is why direct confirmation such as that by Allen and Vignoles (Citation2006) is important. What is peculiar is that these authors, and others, still wish to argue about the relative merits of different indices more than they are willing to state clearly (in their abstract, for example) the significance of their direct replication of my work from a decade earlier. Whichever decent approach is used leads to the same substantive findings as mine. That is crucial in what Allen and Vignoles, and others, have now done. The rest is interesting, but empirically and substantively much less relevant.
2. But they also state that the true level of segregation is lower than I have stated. This is because they use a different metric and so the numbers they generate are smaller (although highly correlated with mine). This unfounded comment by Allen and Vignoles is almost exactly like a claim that someone has overstated a length because they measure it in feet rather than yards. For more on this, see Gorard (Citation2007).
3. Although some readers might think that this perfect correlation between the residuals of D and GS would be obvious from the similarity in their calculations, it is worth stressing here because there are some commentators to whom this identity is not obvious, but who are nevertheless taken seriously by others. Allen and Vignoles (Citation2006), for example, try to portray the two indices as fundamentally different. They are not. And, as this paper shows, unless the distribution of the underlying measure changes fundamentally (as it did in 1992) then they give exactly the same substantive results—as should all decent indices of segregation.
4. Some commentators, again including Allen and Vignoles (Citation2006), might object that using these real‐life data on schools is somehow unfair and that at extremes the values of D and GS would diverge in some way. We have no reason from the formulae, from simulations or from real‐life to expect this perfect correlation to go wrong for any given set of figures. Again, for further discussion of the errors made by Allen and Vignoles (Citation2006), such as those surrounding the boundaries for D and GS, see Gorard (Citation2007).
5. The use of two decimal places in all tables for this paper must not mislead readers of a less numerate disposition into imagining that the variation of less than 5/1000ths between some measures in any one year in Table means that Dt and GSt, for example, cannot correlate at a value within less then 5/1000ths of 1.00 in Table .
6. Figure shows why this difference might matter in an analysis changing indicators between take‐up and eligibility. Of course, an analyst might not want such invariance if their object of study was focused on the differences in trends between segregation by take‐up and by eligibility. As above, each analysis needs to justify its use of an index. There is no one perfect index for all situations.
