以功效函数为主线的假设检验教学
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摘要
本文基于假设检验相关概念的统一,以及初等统计和高等统计学衔接的考虑,提出了以功效函数为主线的教学设计.首先基于证据原理确定拒绝域的形式,计算相应的功效函数;然后用功效函数描述假设检验的两类错误概率;最后根据给定的显著性水平运用功效函数确定拒绝域的具体形式.
Considering the unification of the related concepts and the need of learning Advanced Statistics,this paper proposes the use of power function as the main line in teaching hypothesis testing.We first determine the rejection region based on the evidence principle and calculate the corresponding power function.The probabilities of the two types of errors are described by the power function.Finally,the concrete form of rejection region is determined according to a given significance level.
Considering the unification of the related concepts and the need of learning Advanced Statistics,this paper proposes the use of power function as the main line in teaching hypothesis testing.We first determine the rejection region based on the evidence principle and calculate the corresponding power function.The probabilities of the two types of errors are described by the power function.Finally,the concrete form of rejection region is determined according to a given significance level.
引文
[1]Lehmann E L.Testing Statistical Hypotheses(3th E-dition)[M].New York:Springer,2005
[2]陈希孺,倪国熙.数理统计学教程[M].上海:上海科学技术出版社,1988
[3]魏立力,马江洪,颜荣芳.概率统计引论[M].北京:科学出版社,2012
[4]G.Casella,R.L.Berger.Statistical Inference(2th Edition)[M].北京:机械工业出版社,2002
[5]魏立力,张定强,确定假设检验拒绝域的证据原理[J].数学的实践与认识,2018,48(16):196-200
[2]陈希孺,倪国熙.数理统计学教程[M].上海:上海科学技术出版社,1988
[3]魏立力,马江洪,颜荣芳.概率统计引论[M].北京:科学出版社,2012
[4]G.Casella,R.L.Berger.Statistical Inference(2th Edition)[M].北京:机械工业出版社,2002
[5]魏立力,张定强,确定假设检验拒绝域的证据原理[J].数学的实践与认识,2018,48(16):196-200