中文摘要：

考试评分缺失数据较为常见，如何有效利用现有数据进行统计分析是个关键性问题。在考试评分中，题目与评分者对试卷得分的影响不容忽视。根据概化理论原理，按考试评分规则推导出含有缺失数据双侧面交叉设计（P×i×r）方差分量估计公式，用Matlab7．0软件模拟多组缺失数据，验证此公式的有效性。结果发现：（1）推导出的公式较为可靠，估计缺失数据的方差分量偏差相对较小，即便数据缺失率达到50％以上，公式仍能对方差分量进行较为准确地估计；（2）题目数量对概化理论缺失数据方差分量的估计影响最大，评分者次之，当题目数量和评价者数量分别为6和5时，公式能够趋于稳定地估计；（3）学生数量对各方差分量的估计影响较小，无论是小规模考试还是大规模考试，概化理论估计缺失数据的多个方差分量结果相差不大。

英文摘要：

Missing data are easily found in psychological surveys and experiments such as test scores. For example, in performance as- sessment, a certain group of raters rate a certain group of examinees. By this token, the data from performance assessment compose a sparse data matrix. Researchers are always concerned about how to make good use of the observed data. Brennan （2001） provided the estimating formulas of p x i design of sparse data. But in practice, there is always more than one factor which has an effect on the exper- iment such as the factor of rater and cannot be ignored in the performance assessment. The aim of this article is to find a way that can estimate the variance component of sparse data quickly and effectively. In China, many studies only analyzed complete data and ignored sparse data. There are two merits. Firstly, when facing missing data, researchers usually deleted incomplete records or used imputation before analysis. But using these methods to analyze performance assessment will lose sight of the data which can be used for analysis. Secondly, the estimated value will differ along with different imputation methods. This article provided the estimating formulas of p × i × r design of sparse data, based on the estimating formulas of p x i design of sparse data provided by Brennan （2001）. This article used MATLAB 7.0 to simulate data which were usually encountered in examination, then used the generalizability the- ory to estimate variance components. We simulated two conditions respectively, a small size with 200 students and a large size with 10000 students. We then used the estimating formulas of p × i × r design of sparse data to estimate variance components in order to test the formulas＇ validity. The research showed that these formulas provided a good estimation of variance components. The estimated variance components approach to set values. The accuracy rates of item and rater were the highest. The accuracy rates of interaction of students and items was low. The maximum b