基于分箱测试分数数据的更快估计——以及它们的准确度
Faster Estimates from Binned Test Score Data---and How Accurate They Are
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中文总结 AI 辅助
针对教育测试分数分箱数据，提出R包binest中的fast_hetop()函数，实现快速估计均值和标准差，并分析其准确度，指出在偏斜分布下存在偏差。
中文摘要 AI 辅助
教育机构通常通过统计在3至5个不同分箱中得分的学生人数来总结测试分数分布。HETOP模型假设每个学校或地区的分数服从正态分布，将分箱计数转换为估计的均值和标准差。过去的HETOP实现运行缓慢，在处理德克萨斯州全部1,151个地区的分箱计数时，耗时3至60分钟，甚至可能无法完成。我们在R包binest中的新函数fast_hetop()能在不到一秒的时间内处理所有德克萨斯地区。用户可以选择极大似然、经验贝叶斯、基于样本或基于总体的估计。估计值与真实值高度相关，但当分数分布偏斜且分数集中在最低或最高分箱时，估计存在偏差。
英文摘要
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.
发表机构
- LBJ School of Public Affairs, University of Texas at Austin（德克萨斯大学奥斯汀分校 LBJ 公共事务学院）
机构由 AI 辅助整理，请以论文原文为准。
