This article describes an extension to the use of heteroskedastic ordered probit (HETOP) models to estimate latent distributional parameters from grouped, ordered-categorical data by pooling across multiple waves of data. We illustrate the method with aggregate proficiency data reporting the number of students in schools or districts scoring in…

This paper describes a method for pooling grouped, ordered-categorical data across multiple waves to improve small-sample heteroskedastic ordered probit (HETOP) estimates of latent distributional parameters. We illustrate the method with aggregate proficiency data reporting the number of students in schools or districts scoring in each of a small…

Linking score scales across different tests is considered speculative and fraught, even at the aggregate level (Feuer et al., 1999; Thissen, 2007). We introduce and illustrate validation methods for aggregate linkages, using the challenge of linking U.S. school district average test scores across states as a motivating example. We show that…

Test score distributions of schools or demographic groups are often summarized by frequencies of students scoring in a small number of ordered proficiency categories. We show that heteroskedastic ordered probit (HETOP) models can be used to estimate means and standard deviations of multiple groups' test score distributions from such data. Because…

There is no comprehensive database of U.S. district-level test scores that is comparable across states. We describe and evaluate a method for constructing such a database. First, we estimate linear, reliability-adjusted linking transformations from state test score scales to the scale of the National Assessment of Educational Progress (NAEP). We…

Prior research suggests that males outperform females, on average, on multiple-choice items compared to their relative performance on constructed-response items. This paper characterizes the extent to which gender achievement gaps on state accountability tests across the United States are associated with those tests' item formats. Using roughly 8…

We estimate male-female test score gaps in math and English language arts (ELA) for nearly 10,000 U.S. school districts using state accountability data from third- through eighth-grade students in the 2008-2009 through 2015-2016 school years. We find that the average U.S. school district has no gender achievement gap in math, but there is a gap of…

This paper provides the first population-based evidence on how much standardized test scores vary among public school districts within each state and how segregation explains that variation. Using estimates based on roughly 300 million test score records in math and English Language Arts (ELA) for Grades 3 through 8 from every U.S. public school…

This paper provides the first population-based evidence on how much standardized test scores vary among public school districts within each state and how segregation explains that variation. Using roughly 300 million standardized test score records in math and ELA for grades 3 through 8 from every U.S. public school district during the 2008-09 to…

In the first systematic study of gender achievement gaps in U.S. school districts, we estimate male-female test score gaps in math and English Language Arts (ELA) for nearly 10,000 school districts in the U.S. We use state accountability test data from third through eighth grade students in the 2008-09 through 2014-15 school years. The average…

Has the gap in average standardized test scores between students from high- and low-income families widened, narrowed, or remained stable over the last 3 decades? The question is important both because the achievement gap is measure of how (un)equally educational opportunities are distributed in the US, and because the disparity in educational…

A comparison of Chicago public school students' standardized test scores in 2009-2014 with those of public students across the U.S. reveals two striking patterns. First, Chicago students' scores improved dramatically more, on average, between third and eighth grade than those of the average student in the U.S. This is true for students of all…

Test scores are commonly reported in a small number of ordered categories. Examples of such reporting include state accountability testing, Advanced Placement tests, and English proficiency tests. This paper introduces and evaluates methods for estimating achievement gaps on a familiar standard-deviation-unit metric using data from these ordered…

Test scores are commonly reported in a small number of ordered categories. Examples of such reporting include state accountability testing, Advanced Placement tests, and English proficiency tests. This article introduces and evaluates methods for estimating achievement gaps on a familiar standard-deviation-unit metric using data from these ordered…

In an earlier paper, we presented methods for estimating achievement gaps when test scores are coarsened into a small number of ordered categories, preventing fine-grained distinctions between individual scores. We demonstrated that gaps can nonetheless be estimated with minimal bias across a broad range of simulated and real coarsened data…