Comparative Analysis of Socioeconomic Gaps on Achievement Test Scores: A Rank-Based Approach

Comparative studies of educational inequality often face challenges in ensuring comparability because the marginal distribution of original data in each country sample can affect the estimation of the impact of children's family socioeconomic status (SES) on educational achievement. In this study, we aim to apply rank-based methods to address these problems.

We introduce a theoretical construct called Generalized Socioeconomic Status for Origin (GSESO), which aggregates multiple content dimensions of the socioeconomic status of a child's family, including parental education, parental occupational status (ISEI), household income, and household wealth. Using data from 11 societies in the PISA 2012 survey, we compare the effect of GSESO on children's educational achievements. Given the unidimensional structure of GSESO, we use this unidimensional measure as the independent variable. Testing scores are the dependent variable. For parental education and occupational status, we used the highest value of either parent. Household wealth was measured through a series of possessions aggregated by principal component analysis (PCA). To ensure comparability, we applied percentile ranking transformations to these variables, eliminating the impact of marginal distribution differences across societies. Multiple imputation was used to address missing data problems. We used PCA to test dimensionality and found strong evidence for a one-dimensional composite measure.

According to copula theory, applying percentile ranking transformations to the dependent and independent variables ensures that the parameters of GSESO are free from the marginal distributions in each society, as their percentile rankings follow the uniform distribution. Finally, we use rank-rank regression to estimate the impact of GSESO on educational outcomes.