Using the Gini coefficient for assessing heterogeneity within classes and schools

Abstract

This study demonstrates that the Gini coefficient works as a dispersion measure for gauging educational heterogeneity in and between classrooms and schools. The method for this is to compare Gini coefficients for empirical data from various areas such as gender proportions in upper secondary school programmes and dispersion in achievement within classroom and between schools. The main results are that the Gini coefficient works for gauging heterogeneity on different statistical measurement scales and different sample sizes. An example of small sample is the nominal categories of upper secondary school study programmes, for which the Gini coefficient gauges differences in gender proportions while this sample size should be too small for several other measures of inequality and dispersion. An example of large sample of quotient scale data is two neighbour schools that mainly enrol different achievement strata from the same student cohort. Here the Gini coefficient displays the two schools’ student heterogeneity to be different. An example of moderate size sample is to explore how the teaching group heterogeneity, gauged as Gini coefficient on achievements, re-distributes from within to between classes as the same students proceed from cohesive compulsory school to the students’ individual choice of upper secondary school programmes. Since the Gini coefficient can gauge heterogeneity on small samples, a suggestion for further research is to use it for exploring the relation between strategies for classroom orchestration and levels of classroom heterogeneity, for example between teaching groups at different achievement strata.