学情调查中单项选择题的统计方法  

A Statistical Method for Multiple Choice in Learning Actuality Investigation

作　　者：吴誉[1] 

机构地区：[1]浙江东方职业技术学院工程技术系,浙江温州325011

出　　处：《北京工业职业技术学院学报》2016年第2期23-26,35,共5页Journal of Beijing Polytechnic College

摘　　要：在单选题的统计中,卷面答题正确的人数,一般不同于真正会做该题的人数。利用贝叶斯条件概率推导出真正会做的人数、卷面答题正确的人数、选择题选项三者之间的关系式,解决从答题的简单统计结果中,计算出真正会做题的人数的问题。借助二项分布概率模型,对于关系式的边界情况,做出有效性的证明。借助学情调查问卷的一个逻辑推理题统计的实际案例,验证该关系式的实用性。研究结果能够更加准确地提取学情调查中的信息,为教学环节、教学活动、教学方式等教改基础工作,提供较为准确的依据。Generally,in statistics of the multiple choice questions,the number of students who merely answered correctly is not equal to the number of those who really understand. A mathematic formula derived from the Bayes＇ theorem hereby,can effectively express the relationship among the number of the understanding students,the number of the correct- answer students and the number of options. Furthermore it can count up the number of the understanding people from the simply statistics of the quiz results. By the binomial distribution,this formula is also proved to be valid in boundaries. Then,the article illustrates that the formula is useful to analyze the learning actuality,taken the statistic of logical inference questions in a freshmen investigation as an example. The research result can extract the more exact information in student analysis investigations. Meanwhile it can provide a more accurate starting point for the teaching works.

关 键 词：学情 选择题 条件概率 二项分布 

分 类 号：O21[理学—概率论与数理统计]