Measuring ‘equity’ and ‘equitability’ in school effectiveness research

Abstract

This paper introduces a Gini-type index for measuring ‘attainment equity’ in schools; that is to say, how far a school (or group of schools) is from having a ‘fair’ proportion of its examination success attributable to a fair proportion of its student population. Using data from the National Pupil Database, the Index is applied to more than 20,000 students with matched attainment records at KS2 and KS4 in two ‘statistical-neighbour’ local authorities in England, capturing the extent to which they are meeting a public policy notion of equity. It is then combined with existing contextual value added measures to analyse school and local authority performance in terms of both attainment equity and context.

Acknowledgements

I would like to thank Pam Sammons and Daniel Muijs for their helpful discussions.

Notes

1. The term is not uncontested and is explored in the paper.

2. The ‘General Certificate in Secondary Education’ is the examination taken by nearly all 16-year-old pupils in England and Wales after (typically) five years of secondary schooling.

3. Compulsory schooling in England is divided into ‘Key Stages’: KS1 (Years 1 and 2) for ages 5–7; KS2 (Years 3–6) for ages 7–11; KS3 (Years 7–9) for ages 11–14; KS4 (Years 10 and 11) for ages 14–16.

4. GCSE data in the UK is available in different ‘bundles: the percentage of grades A^∗–C across all subjects; the percentage of grades A^∗–C including English and mathematics; the (‘capped’) percentage of grades A^∗–C in pupils’ best eight subjects; and so forth. In this paper, we are using the first of these (viz. the simple percentage of grades A∗–C obtained across all subjects) because it is the metric most frequently valued by UK policy-makers in measuring rates of progression to post-compulsory and higher education, themselves held to be measures of equity in the system (e.g. HEFCE, 2005, 2010; Access 2008; Thompson 2010).

5. In particular, Rawls’s Second Principle of Justice—that socioeconomic inequalities should be arranged so that they are of the greatest benefit to the least advantaged members of society—the basis of which is the view that ‘arbitrary factors’ like innate intellectual ability and the benefits that derive from it, should not determine life-chances or opportunities. Critiques of the Rawlsian view by Nozick (1974), Sandel (1982) and others would not negate this interpretation of Rawls’s theory in relation to educational attainment.

6. The trapezoids in question each have area ½(X_k - X_k-1)(Y_k + Y_k-1).

7. In the case of the quadratic function y² = x, area A+B = ₀∫¹ ydx = 2/3.

8. The problem is analogous to the system of scoring value-added in the UK, where a negative result would be possible but for the fact that 100 is added to KS1–KS2 scores and 1000 is added to KS2–KS4 scores.

9. A total of 9.9% of pupil entries had incomplete data with regard to either GCSE or KS2 attainment. These were removed from the dataset.

10. The Index could be adapted to incorporate shrinkage measures (e.g. Kreft, 1996; DfES/Ofsted, 2004; Thomson, 2007) for small cohorts, which would cause their data to be moved closer to the mean and make it less likely that extreme scores were recorded.

11. It would have been possible to calculate Æ indices for hundreds of schools and local authorities in the NPD, but at such an early stage of developing and trialling the concept, it was more important to test for ‘face validity’, to which end the concepts and findings were presented to managers and headteachers from the LA/schools in question, who confirmed very strongly their value. This would not have been possible with a large number of schools/authorities.

12. The indices are given correct to three significant figures, but there is no suggestion that the measure is representative of that degree of precision. Local authority-wide indices were also calculated using GCSE A^∗–G (shown on the Tables), which, as expected, were lower in both authorities since the spread of lower-grade attainment was proportionately more attributable to low-attaining pupils.

13. The Income Deprivation Affecting Children Index (IDACI) is based on student home post-codes and is essentially a measure of the proportion of children under 16 living in families in receipt of at least one of a specified range of social welfare measures, including income support, job seeker’s allowance, working families’ tax credit and disabled person’s tax credit. It is closely correlated to %FSM. The IDACI ranges in value from 0 to 1, with a national average of approximately 0.14 (National Statistics, 2006).

14. The Æ indices were predictably lowest for the two schools with a selective element: school ‘C’ in Southampton and school ‘K’ in Portsmouth.

15. The peaks in both trend graphs in 2005–2006 may reflect changes in GCSE qualification ‘equivalency’ kicking in at that time, which is itself interesting as it shows a worsening of the situation in equity terms between high- and low-(prior) attaining pupils.

16. But what follows could apply just as easily to %EAL or %SEN or to any ‘percentagized’ impact factor.

17. It is possible to develop adjustments with ceilings, although this would mean departing from the linearity of the ‘ideal’ and from the notion of an index warranted by school effects research.

18. Equity’ (noun): fairness; ‘Equitable’ (adjective): having equity; ‘Equitability’ (noun): in this sense, the capability of individuals to benefit from the unbiased distribution of equity.

19. The phrase ‘high equity school’ used in a positive sense, as is usually the case, is surely misleading, as a uniformly ineffective school failing all its pupils equally is hardly worthy of praise. The mistake is to confuse ‘sharing’ with ‘sharing success’.

20. See reports from the London Challenge (DfES, 2003, 2006a, 2006b; Ofsted 2010), though it is striking that there are no references in any of these reports to equity, equitability or equality.