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.