Ordinal Approaches to Decomposing Between-group Test Score Disparities

November 2020

The estimation of test score “gaps” and gap trends plays an important role in monitoring educational inequality. Researchers decompose gaps and gap changes into within- and between-school portions to generate evidence on the role schools play in shaping these inequalities. However, existing decomposition methods assume an equal-interval test scale and are a poor fit to coarsened data such as proficiency categories. This leaves many potential data sources ill-suited for decomposition applications. We develop two decomposition approaches that overcome these limitations: an extension of V, an ordinal gap statistic, and an extension of ordered probit models. Simulations show V decompositions have negligible bias with small within-school samples. Ordered probit decompositions have negligible bias with large within-school samples but more serious bias with small within-school samples. More broadly, our methods enable analysts to (1) decompose the difference between two groups on any ordinal outcome into portions within- and between some third categorical variable, and (2) estimate scale-invariant between-group differences that adjust for a categorical covariate.

Education level

K-12 Education

Topics

Methods