ABSTRACT

In recent years, the interest in measuring growth in student ability in various subjects between different grades in school has increased. Therefore, good precision in the estimated growth is of importance. This paper aims to compare estimation methods and test designs when it comes to precision and bias of the estimated growth of mean ability between two groups of students that differ substantially. This is performed by a simulation study. One- and two-parameter item response models are assumed and the estimated abilities are vertically scaled using the non-equivalent anchor test design by estimating the abilities in one single run, so-called concurrent calibration. The connection between the test design and the Fisher information is also discussed.

The results indicate that the expected a posteriori estimation method is preferred when estimating differences in mean ability between groups. Results also indicate that a test design with common items of medium difficulty leads to better precision, which coincides with previous results from horizontal equating.

摘要

近年来，人们越来越关注衡量学校不同年级之间各个科目的学生能力增长情况。因此，估计增长的精确度非常重要。本文旨在比较两组差异显着的学生的平均能力估计增长的精度和偏差时的估计方法和测试设计。这是通过模拟研究来执行的。假设有一个和两个参数的项目响应模型，并且使用非等效锚测试设计通过在一次运行中估计能力（所谓的并发校准）来垂直扩展估计的能力。还讨论了测试设计和 Fisher 信息之间的联系。

结果表明，在估计组间平均能力的差异时，首选预期的后验估计方法。结果还表明，具有中等难度的常见项目的测试设计会带来更好的精度，这与先前的水平等式结果一致。