Testing programs are often interested in using a student growth measure. This article presents analytic derivations of the accuracy of common student growth measures on both the raw scale of the test and the percentile rank scale in terms of the proportional reduction in mean squared error and the squared correlation between the estimator and target. The study contrasts the accuracy of the growth measures against that of current status measures—current test scores and their percentile ranks. Key findings include the extent that status measures are more accurate than any of the growth measures and that alternative methods to estimate growth could be more accurate than the currently used methods. Our findings highlight the importance for evaluating the statistical properties of growth measures along with other concerns for states that are debating the reporting of growth. Our results also point out that assessing the accuracy of growth measures requires the specification of quantities of interest in terms of latent achievement rather than observed test scores, which is common practice for developing status measures but essentially never done by testing programs for growth measures.

中文翻译：

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比较学生成长测度的准确性

测试程序通常对使用学生成长测度感兴趣。本文通过均方误差的比例减少以及估计量与目标之间的平方相关性，介绍了在测试原始量表和百分位数等级量表上普通学生成长测度的准确性的解析推导。该研究将增长指标与当前状态指标（当前测试分数及其百分数等级）的准确性进行了对比。主要发现包括：程度指标比任何增长指标都更准确，以及估计增长的替代方法可能比当前使用的方法更准确。我们的发现凸显了评估增长测度的统计属性的重要性以及对正在讨论增长报告的各州的其他担忧。我们的结果还指出，评估增长测度的准确性需要根据潜在成就而不是观察到的测试分数来指定感兴趣的数量，这是开发状态测度的常见做法，但从根本上不通过测试测度计划来完成。