Measuring equity in educational effectiveness research: the properties and possibilities of quantitative indicators

Abstract

There has never been a published discursive review of equity measurement methodology in educational effectiveness research, though the literature on equity is growing. This paper sets out several indices that have the potential to measure it in terms of pupil attainment or in terms of how far a school (or group of schools) is from having a ‘fair’ proportion of its success attributable to a ‘fair’ proportion of its student population. The paper explores the principles and properties of three relatively simple metrics (the Range Ratio family of measures, the Coefficient of Variation, and McLoone’s Index) leading to two complex measures (Theil’s T and finally to the Gini-based Attainment Equity Index). The paper investigates the warrant that the measures have (or do not have) for measuring equity by exploring them in a theoretical way so that their strengths, provenances and presumptions reveal themselves, and concludes with a discussion – the first of its kind in educational effectiveness research - on their desirable characteristics and properties. Worked examples from 2009 and 2011 UK pupil attainment data are presented in the Notes by way of worked illustration, as are another two indices: the Variance of the Logs and the Atkinson Index.

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ORCID for Anthony Kelly: orcid.org/0000-0003-4664-8585

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