Two related measures of educational inequality are proposed: one for educational achievement and another for educational opportunity. The former is the simple variance (or standard deviation) of test scores. Its selection is informed by consideration of two measurement issues that have typically been overlooked in the literature: the implications of the standardization of test scores for inequality indices, and the possible sample selection biases arising from the Program of International Student Assessment (PISA) sampling frame. The measure of inequality of educational opportunity is given by the share of the variance in test scores that is explained by pre-determined circumstances. Both measures are computed for the 57 countries in which PISA surveys were conducted in 2006. Inequality of opportunity accounts for up to 35 percent of all disparities in educational achievement. It is greater in (most of) continental Europe and Latin America than in Asia, Scandinavia, and North America. It is uncorrelated with average educational achievement and only weakly negatively correlated with per capita gross domestic product. It correlates negatively with the share of spending in primary schooling, and positively with tracking in secondary schools.
Ferreira, F.H.G.; Gignoux, J. The Measurement of Educational Inequality: Achievement and Opportunity. The World Bank Economic Review (2013) 28 (2) 210-246. [DOI: 10.1093/wber/lht004]
The Measurement of Educational Inequality: Achievement and Opportunity