临界域形状选择与犯第Ⅱ类错误的概率的一个重要结果

A IMPORTANT RESULT ABOUT SHOOSE OF CRITICAL REGION AND PROBABILITY OF MAKING SECOND KIN MISTAKE

统计问题总是从样本去推断总体的性质.除参数估计外,假设检验也是一种重要的推断形式.从理论上而言,它也是数理统计的一个分支.本文就临界域特别是双侧检验临界域的形状的选择与犯第Ⅱ类错误的关系进行初步探讨.得到的结论是:临界域的左右两部分与统计量密度曲线间所夹面积各为α1,α2时(α1+α2=α)(其中α为显著性水平),犯第Ⅱ类错误的概率可大可小,与检验的参数的真值有一个明确的依赖关系.

The property of sample space can always be inferred from samples in statistical problems. In addition to parameter estimation, hypothesis testing is also an important inference method, and it is a branch of mathematical statistics by theory. In this paper, a primary discussion on relation between choosing two-sided test critical region and making second kind mistake is shown. We get conclusions that suppose one area which is circled by left parts and statistic density curve is α_1 and the other area which is circled by right parts and statistic density curve is α_2, and α_1+α_2=α is level of significance, probability of making second kind mistake is indefinite and it has a definite dependent relation to parameter real value which is tested.