Ordinal Approaches to Decomposing Between-Group Test Score Disparities

David M. Quinn, Andrew D. Ho

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)466-500
Number of pages35
JournalJournal of Educational and Behavioral Statistics
Issue number4
StatePublished - Aug 2021
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2020 AERA.


  • achievement gap
  • decomposition
  • ordinal decomposition
  • ordinal methods
  • simulation study
  • test score gap


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