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 to 2011 UK pupil attainment data are presented in the Notes by way of worked illustrations, as are another two indices: the Variance of the Logs and the Atkinson Index.

Educational process factors for effective education in resource-constrained countries: a multilevel analysis

“…Moreover, the fact that the Theils T is associated with a higher marginal utility of equity for transfers from the 'have-lots' to the 'have-nots' could be of paramount importance to policy making in resource-constrained countries, where the 'havenots' form the majority. Nonetheless, this is also a weakness, as it fails to demonstrate the transferability property (Kelly, 2015). Moreover, its range is from zero to positive infinity, making interpretation and comparability complex.…”

“…A number of metrics have been suggested by which to measure inequity in education. (2007), Kelly (2012), Kelly (2015), Agrawal (2014), Gorard and Smith (2004), Haughton and Khandker (2014), and Kyriakides and Creemers (2011) provide a variety of metrics for educational inequity. These include the range, the range ratio, the coefficient of variation, the variance, the standard deviation, the correlation coefficient, the McLoone index, the Gini coefficient, the Theil index, the regression slope, the Lorenz curve and the attainment equity, among others.…”

“…Though there are a variety of metrics to measure inequity in education, there are common themes in the formulation of these measures, such as the deviation, dispersion, skewness and variance from the norm. The choice of the measure will always be guided by, among others, the principal cause of inequity, the equity definition adopted, the level at which policies are actualised, the robustness of the measure, the nature and availability of data, the kind of question on inequality being answered and, sometimes, value judgements (Haughton and Khandker, 2014;Kelly, 2015). Further, Kelly (2015) indicates that the transferability, scale invariance and decomposability of the metric could also affect choice of equity metrics.…”

“…To illustrate, the education Gini is mean independent, independent of population size, symmetrical and fulfils the Pigou-Dalton transfer sensitivity property (Haughton and Khandker, 2014;Hale, 2003). Moreover, it has a definite scale, which makes it easier to interpret than other measures that vary to infinity (Kelly, 2015). Most importantly, it is applicable to both cross-sectional and longitudinal datasets.…”

“…v i /μ is the ratio of individual school inputs value to the sample mean inputs and the natural log of v i /μ determines whether that individual school Theils T element is positive (when individual school inputs value is greater than the sample inputs mean), negative when otherwise or zero when the two are equal (every individual school has exactly the same as the group average) (see Kelly, 2015).…”