基于离散化误差补偿的试题难度题量控制方法

自动组卷是高校实现考试规范化、科学化的重要手段。考生的平均成绩可以通过试卷的平均难度来控制。然而，如何确定各种难度的题量是关键技术。利用正态分布来确定各种难度的题量，是目前研究的一个方向。提出了对难度进行离散化正态分布后，利用对称积分求取各种难度的概率分布，并且采用比例误差补偿方法减少误差。同时，根据自动组卷的具体问题，确定了标准差取0. 2更加合适，并且给出了在不同的总题量下各种难度题量的分配方案。结果表明，基于离散化误差补偿的试题难度题量控制方法能够较好地控制各种难度的题量，为自动组卷策略提供了有效的依据。

Discrete Error Complementary Strategy Based Control Method to Quantify Various Difficulty Levels of Test Questions

It is extremely important to auto-generation examination papers for high school,with the purpose of making examination normative and scientific. The average scores of students can be controlled by average difficulty level of the examination paper. However, how to quantify various difficulty levels of test questions is a key step. Currently, a common strategy is to adopt normal distribution to specify those numbers. After discretizing the normal distribution function based on the difficulty factor, the probability distributions of various difficulty levels were obtained according to symmetrical integral and a proportion error complementary method was adopted to reduce errors. According to the analysis results in the auto-generation examination papers, the standard deviation of 0. 2 is more suitable. In last, the computed numbers of various difficulty levels of test questions arc listed in various total questions. The result shows that the control method that use discrete error complementary strategy can control the ctuantity of various difficulty levels of test questions well and enable the strategy of auto-generation examination papers to be effective.