Faster Estimates from Binned Test Score Data---and How Accurate They Are
Abstract
Education agencies often summarize test score distributions by counting how many students scored in 3 to 5 different \textit{bins}. The HETOP model transforms bin counts into estimated means and standard deviations, assuming that scores follow a normal distribution within each school or district. Past HETOP implementations ran slowly, taking 3--60 minutes, if they finished, when given bin counts for all 1,151 districts in Texas. Our new function, \code{fast\_hetop()} in the R package \pkg{binest}, runs all Texas districts in less than a second. Users can choose between maximum likelihood, empirical Bayes, sample-based or population-based estimates. Estimates are strongly correlated with true values, but have bias when the score distribution is skewed and scores are concentrated in the lowest or highest bin.
Related
- The Debiased Score Test: Hunt-and-test for Semiparametric Hypotheses
- Discrete p-Fold Directional Models for Binned Orientation Data with Applications to Sand-Grain Orientations and Urban Street Networks
- Discrete quadrature spectrum of composite bosons: Weyl relation, intensity correlations, and binned homodyne detection
- Get Permanent Results Faster by Counting Stars
- Faster high-accuracy multicommodity flow in dense graphs
BibTeX
@misc{hippel2026faster,
title = {{Faster Estimates from Binned Test Score Data---and How Accurate They Are}},
author = {Paul T. von Hippel},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36312},
eprint = {2609.36312},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36312},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Faster Estimates from Binned Test Score Data---and How Accurate They Are
AU - Paul T. von Hippel
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.36312
UR - https://arxiv.org/abs/2609.36312
AB - Education agencies often summarize test score distributions by counting how many students scored in 3 to 5 different \textit{bins}. The HETOP model transforms bin counts into estimated means and standard deviations, assuming that scores follow a normal distribution within each school or district. Past HETOP implementations ran slowly, taking 3--60 minutes, if they finished, when given bin counts for all 1,151 districts in Texas. Our new function, \code{fast\_hetop()} in the R package \pkg{binest}, runs all Texas districts in less than a second. Users can choose between maximum likelihood, empirical Bayes, sample-based or population-based estimates. Estimates are strongly correlated with true values, but have bias when the score distribution is skewed and scores are concentrated in the lowest or highest bin.
ER -