二项双侧检验不同拒绝域选取研究  

The different rejection region study of two-sided binomial test

作　　者：方红燕 靳立帅 朱颖 李晓琴[1] FANG Hongyan;JIN Lishuai;ZHU Ying;LI Xiaoqin(School of Big Data and Statistics,Anhui University,Hefei Anhui 230601,China)

机构地区：[1]安徽大学大数据与统计学院,安徽合肥230601

出　　处：《阜阳师范大学学报（自然科学版）》2023年第2期1-6,共6页Journal of Fuyang Normal University:Natural Science

基　　金：国家自然科学基金(11801003);安徽省自然科学基金(2008085MA14);安徽大学大学生创新创业训练项目(X202210357001)资助。

摘　　要：假设检验理论是数理统计知识体系中很重要的一环。在双侧假设检验问题中,对于拒绝域的构造通常是采用二分法的形式来得到,其优点是理论简单并且容易操作。但在零假设下统计量的分布为非对称分布情形下,由区间估计理论知通过二分法构造的区间长度并非最优。已知概率参数不等于0.5的二项分布并非对称分布,以二项检验中的双侧假设检验问题为例,分别用二分法和最短距法构造双侧检验的拒绝域进行研究,模拟比较二者的I型错误和检验功效情况。实验结果表明:最短距法构造的拒绝域对应的检验其I型错误更加稳健,检验的功效也更高。Hypothesis Testing Theory is an important part in statistic theory.In two-sided hypothesis testing problems,the construction of the rejection domain is usually obtained in the form of a dichotomy,which has the advantage of being simple theoretically and easy to manipulate.Nevertheless,the interval length constructed by the dichotomy is not the optimal one according to the interval estimation theory,especially when the distribution of the test statistic under the null hypothesis is not symmetric.Given that the binomial distribution whose probability parameter is not equal to 0.5 is not symmetrical,the binomial hypothesis testing problem is taken as an example,and the rejection domain of the binomial test is constructed by the dichotomy method and the shortest distance method respectively to simulate and compare their type I errors and test efficacy.The simulation result show that the test with rejection region generated by the shortest length method has more precise type I error rate and higher testing power.

关 键 词：假设检验 拒绝域 P值 二项检验 双侧检验 检验功效 

分 类 号：O212.1[理学—概率论与数理统计]