@EdWorkingPaper{ai20-257,
title = "Ordinal Approaches to Decomposing Between-group Test Score Disparities",
author = "David M. Quinn, Andrew D. Ho",
institution = "Annenberg Institute at Brown University",
number = "257",
year = "2020",
month = "July",
URL = "http://www.edworkingpapers.com/ai20-257",
abstract = {Researchers decompose test score “gaps” and gap-changes into within- and between-school portions to generate evidence on the role that schools play in shaping educational inequality.  However, existing decomposition methods (a) assume an equal-interval test scale and (b) are a poor fit to coarsened data such as proficiency categories. We develop two decomposition approaches that overcome these limitations: an extension of V, an ordinal gap statistic (Ho, 2009), and an extension of ordered probit models (Reardon et al., 2017). 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. These methods are applicable to decomposing any ordinal outcome by any categorical grouping variable.},
}