基于随机占优理论的地区教育水平比较

Comparison of Regional Education Levels Based on Theory of Stochastic Dominance

高考一直是中国社会关注度很高的民生话题,比较不同地区高考表现,从而衡量地区教育发展水平高低的价值性很高.常见的做法是使用均值、中位数和方差等统计量来比较.但这些方法过于粗糙,一方面很多数据之间无法直接比较,另一方面,由于依赖于特定总体分布类型,当这些假设不成立时容易得到错误的结论.本文基于随机占优检验理论,结合2021全国大学入学考试的成绩数据,比较了A,B,C,D四个省份的考生表现,发现在显著性水平α=0.05之下,1)A省理科成绩一阶随机占优于C省和D省,B省理科成绩一阶随机占优于D省;2)A省理科成绩二阶随机占优于B省,C省和D省,B省理科成绩二阶随机占优于C省和D省;3)A省文科成绩一阶随机占优于C省,B省文科成绩一阶随机占优于D省;4)A省文科成绩二阶随机占优于B省,C省和D省,B省文科成绩二阶随机占优于C省和D省,C省文科成绩二阶随机占优于D省.

The National College Entrance Examination has always been a topic of high concern to people's livelihood in Chinese society,and it is of high value to compare the performance of college entrance examinations in different regions to measure the level of regional education development.It is a common practice to use statistics such as mean,median and variance to compare,but these methods are too coarse as they rely on particular types of population distributions.As a result,they may lead to wrong conclusions.Based on the theory of stochastic dominance,this paper compares the performance of candidates among four different provinces using score data of 2021 National college Entrance Examination in China,and gets some conclusions under the significance level ofα=0.05.Firstly,the performance of science in province A first-order stochastic dominates that of province C and province D.The performance of science in province B first-order stochastic dominates that of province D.Secondly,the performance of science in province A second-order stochastic dominates that of province B,province C and province D.The performance of science in province B second-order stochastic dominates that of province C and province D.Thirdly,the performance of liberal arts in province A first-order stochastic dominates that of province C.The performance of liberal arts in province B first-order stochastic dominates that of province D.Fourthly,the performance of liberal arts in province A second-order stochastic dominates that of province B,province C and province D.The performance of liberal arts in province B second-order stochastic dominates that of province C and province D.The performance of liberal arts in province C second-order stochastic dominates that of province D.