形成性评价(formative evaluation)伴随着我国新一轮的教育改革，逐步深入到 教学实践环节，而有效测量工具和方法的开发和应用可以提高形成性评价的效率。 认知诊断评估(Cognitive Diagnosis Assessment, CDA)的本质在于以认知心理学为 基础，通过构建测量模型和数学算法，依据被试的作答反应对其知识状态进行分 类诊断，为形成性评价提供了方法学基础。认知诊断方法按照是否需要进行参数 估计而分为参数化方法和非参诊断方法。参数化方法因其样本量要求高、模型过 于复杂等，不适合应用于小规模的教学情境(即教学人数或者空间处于班级及以 下规模的教学情境)。然而，具有前提假设弱、计算简明、对样本量要求不高等优 势的非参诊断方法则更适用于对小规模教学情境中的认知诊断。目前，国内外学 者已经将多种非参诊断方法应用于认知诊断中，如，海明距离法(Hamming distance)、曼哈顿距离诊断法(Manhattan distance discrimination, MDD)、K-means 聚类分析法、GNPC 法(General Nonparametric Parameterized Classification，GNPC) 等。此外，机器学习算法常用于数据分类，符合认知诊断对学生的知识状态进行 分类的本质，因此，也有不少学者将机器学习算法应用于认知诊断中，例如，概 率神经网络法(Probabilistic Neural Networks, PNN)等。 非参诊断方法在不同条件下具有良好的稳健性是应用于小规模教学情境的 关键。然而，在实际测验编制过程中，涉及到的测验 Q 矩阵设计，难免会存在误 设的情况。经过对文献的梳理，未发现基于海明距离的非参认知诊断法在不同 Q 矩阵误设类型下的稳健性研究公开发表，也未发现对加权海明距离法、GNPC 法 在不同 Q 矩阵误设比例下判准率的影响研究。因此，本研究囿于已有研究的局 限，设计两个 Monte Carlo 模拟研究：研究一以 10%和 20%的误设比例对一般海 明距离法、加权海明距离法以及 GNPC 法进行稳健性探索；研究二以属性缺失、 属性冗余和属性冗余且缺失这 3 种误设类型作为自变量，固定误设比例为 10% 条件下分析 Q 矩阵误设对上述 3 种方法的影响。 经过研究，得出研究结论如下： (1)一般海明距离法、加权海明距离法以及 GNPC 法的判准率结果不依赖于 测试的样本量，这表明上述 3 种方法可以很好地应用于小规模教学情境中。 (2)3 种方法在 Q 矩阵存在误设的情况下稳健性较强，其中 GNPC 法的稳健 性表现与数据模拟的底层模型有关，GNPC 法在复杂模型下的 PAR 表现优于其余两种方法。 (3)3 种方法在 20%误设比例条件下的 PAR 降幅大于 10%误设比例下的，并 且 PAR 降幅会随着层级关系松散程度的增大而增大。 (4)3 种方法在不同的 Q 矩阵误设类型下的 PAR 降幅不同，当项目个数较多 时，属性冗余且缺失的情况产生的 PAR 降幅位于属性冗余、属性缺失之间。 (5)根据不同的层级关系，在 3 种误设类型下的 PAR 降幅变化也存在差异。 总而言之，在 Q 矩阵存在误设的情况下，一般海明距离法和加权海明距离法， 以及 GNPC 法的稳健性表现仍良好。此外，上述 3 种方法在不同的样本量下认 知诊断判准率也较高，故这 3 种方法适用于小规模教学情境，为教学实践环节中 的学生过程评价提供技术参考。

Formative evaluation is accompanied by a new round of education reform in our country, and it gradually penetrates into the teaching practice processes, and the development and application of effective measurement tools and methods can improve the efficiency of formative evaluation. The nature of Cognitive Diagnosis Assessment (CDA) is based on cognitive psychology, by way of constructing measurement models and mathematical algorithms, and basing students’ response responses to classify and diagnose their knowledge status, so CDA provide methodological basis for formative evaluation. Parametric methods are not suitable for small-scale teaching situations (that is, teaching situations where the number of teachers or the space is in the class and below) because of its high sample size requirements and too complex models. However, non-parametric diagnosis methods that have the advantages of weak premises, simple calculations, and low sample size requirements are more suitable for cognitive diagnosis in small-scale teaching situations. At present, scholars have applied a variety of non-parametric diagnostic methods to cognitive diagnosis, such as Hamming distance, Manhattan distance discrimination (MDD), and K-means cluster analysis. GNPC method (General Nonparametric Parameterized Classification, GNPC), etc. In addition, machine learning algorithms are long used for data classification, which is in common with the essence of cognitive diagnosis to classify students' knowledge status. Therefore, many scholars also apply machine learning algorithms to cognitive diagnosis, such as Probabilistic Neural Networks (Probabilistic Neural Networks). Neural Networks, PNN) etc. The non-parametric diagnosis method has good robustness under different conditions is the key to its application in small-scale teaching situations. However, in the actual test preparation process, the Q matrix design involved in the test will inevitably be misconfigured. After reviewing the literature, it was found that the non-parametric cognitive diagnosis method based on Hamming distance has not be published publicly under different Q-matrix misspecified types, nor has it been found that the weighted Hamming distance method and GNPC method are used in different Q matrices. Research on the influence of the accuracy rate under the wrong ratio. Therefore, this study is limited by the limitations of existing studies, and two Monte Carlo simulation studies are designed: Study one uses the 10% and 20% ratios to perform robustness of the general Hamming distance method, weighted Hamming distance method, and GNPC method. Exploring; Research 2 takes three types of misconfigurations: missing attributes, redundant attributes, and redundant and missing attributes as independent variables, and analyzes the influence of Q-matrix misspecified on the above three methods under the condition of a fixed rate of 10%. The research conclusions are as follows: (1) The accuracy results of the Hamming distance method, weighted Hamming distance method and GNPC method do not depend on the sample size of the test, which shows that the above three methods can be well applied in small-scale teaching situations. (2) The three methods are more robust when the Q matrix is misspecified. The robustness of the GNPC method is related to the underlying model of the data simulation, and the PAR of the GNPC method under the complex model is better than the other two methods. (3) The PAR reduction of the three methods under the condition of 20% ratio is greater than that of 10% ratio, and the PAR decrease will increase with the looseness of the hierarchical relationship. (4) The three methods have different PAR reductions under different Q-matrix misspecified types. When the number of items is large, the PAR reduction caused by the redundant and missing attributes lies between the redundant and missing attributes. (5) According to different hierarchical relationships, there are also differences in PAR reduction changes under the types of Q-matrix misspecified.