Ordinal Approaches to Decomposing Between-Group Test Score Disparities

David M. Quinn and Andrew D. Ho
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David M. Quinn: University of Southern California
Andrew D. Ho: Harvard Graduate School of Education

Journal of Educational and Behavioral Statistics, 2021, vol. 46, issue 4, 466-500

Abstract: 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.

Keywords: ordinal decomposition; achievement gap; test score gap; decomposition; ordinal methods; simulation study (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:sae:jedbes:v:46:y:2021:i:4:p:466-500

DOI: 10.3102/1076998620967726

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