假设检验中两类错误分析与实验  

Analysis and Experiment of Two Kind Errors in Hypothesis Test

作　　者：卢亚丽[1] 

机构地区：[1]华北水利水电学院管理与经济学院,河南郑州450011

出　　处：《河南教育学院学报（自然科学版）》2011年第3期9-12,共4页Journal of Henan Institute of Education(Natural Science Edition)

基　　金：华北水利水电学院管理与经济学院青年教师培养专项基金(2010年11月-2013年11月)

摘　　要：依据小概率原则、中心极限定理以及抽样分布理论,研究了假设检验中犯"弃真"错误概率α、犯"取伪"错误概率β以及样本容量n之间的数量相依变化关系,并给出了它们之间数量关系的具体表达式.设计了显著性检验的数值试验,并给出了相应的MATLAB程序代码.结果表明:n固定时,α和β之间是此消彼长关系;对于固定的α,要降低β就必须增大样本容量n;通过计算总体期望的估计值与实际值的绝对误差,可以给出犯"取伪"错误概率的近似估计.由数值试验计算出的犯"取伪"错误的频率与给出的数学公式计算结果基本吻合.Based on minor probability principle, central-limit theorem, and sampling-distribution theory, studied relations depending on quantity variation among the probability α of violating-TRUE mistakes, the probability β of taking-FALSE mistakes, and sample size n in hypothesis test. Specific expression among them was also given. In addition, designed numerical experiment of significant test and gave the corresponding MATLAB code. Results show that for the fixed n, the α＇ s loss is β＇ s gain. For the fixed α and in order to decrease β, one must increase sample size n. By estimating absolute error between the expectation value and actual value of ensemble, the probability of taking-FALSE mistakes can be approximately calculated. The frequency of taking-FALSE mistakes obtained by numerical experiments is in accord with the result calculated via mathematical formula.

关 键 词：假设检验 “弃真”错误 “取伪”错误 小概率原则 数值试验 

分 类 号：O212.2[理学—概率论与数理统计]