The comparability of the scores obtained in different forms of a test is certainly an essential requirement. This paper proposes a statistical test for the detection of noncomparable scores based on item response theory (IRT) methods. When the IRT model is fit separately for different forms of a test, the item parameter estimates are expressed on different measurement scales. The first step to obtain comparable scores is to convert the item parameters to a common metric using two constants, called equating coefficients. The equating coefficients can be estimated for two forms with common items, or derived through a chain of forms. The proposal of this paper is a statistical test to verify whether the scale conversions provided by the equating coefficients are as expected when the assumptions of the model are satisfied, hence leading to comparable scores. The method is illustrated through simulation studies and a real-data example.

中文翻译：

---

测试链等式的差异

在不同形式的测试中获得的分数的可比性当然是一个基本要求。本文提出了一种基于项目反应理论 (IRT) 方法检测不可比较分数的统计检验。当 IRT 模型分别适合不同形式的测试时，项目参数估计值在不同的测量尺度上表示。获得可比较分数的第一步是使用两个常量将项目参数转换为通用度量，称为等同系数。可以为具有共同项目的两种形式估计等同系数，或者通过一系列形式推导。本文的提议是一项统计测试，用于验证等式系数提供的尺度转换是否符合模型假设时的预期，因此导致可比较的分数。该方法通过模拟研究和真实数据示例进行说明。