Sensitivity Comparisons among Tests of the General Linear Hypothesis
Sensitivity Comparisons among Tests of the General Linear Hypothesis
复制标题
DOI：
10.1080/01621459.1966.10480878
复制
发表时间：
1966-06
影响因子：
3.7
通讯作者：
M. Schatzoff
中科院分区：
文献类型：
--
作者：
M. Schatzoff
Dempster和Schatzoff(4)提出检验的预期显著性水平（expected significance level， ESL），作为比较竞争检验统计量敏感性的标准，定义为在简单替代假设下观察到的显著性水平的期望值。例如，假设h0: X ~ F(X)对h1: X ~ G(X)的下尾检验的ESL由nF(X)dG(X)给出。本文通过模拟各种参数化条件下的ESL，比较了几种提出的一般线性假设检验的灵敏度。结果表明，Wilks的似然比标准A和Hotelling的t02在广泛的备选方案中提供了大致相同的保护水平，而Roy的最大特征根被证明对涉及多个非零根的备选方案相当不敏感。根据ESL标准判断，其他建议的测试统计数据显示不那么敏感。
Abstract The expected significance level (ESL) of a test, proposed by Dempster and Schatzoff (4) as a criterion for comparing sensitivities of competing test statistics, is defined as the expected value of the observed significance level under a simple alternative hypothesis. For example, the ESL of a lower tailed test of the hypothesis H 0: X∼F (x) against H 1: X∼G (x) is given by nF(x)dG(x). In this paper, the sensitivities of several proposed tests of the general linear hypothesis are compared by simulating their ESL's under a wide variety of parameterizations. The results indicate that Wilks's likelihood ratio criterion A and Hotelling's T 0 2 provide about the same levels of protection over a wide spectrum of alternatives, whereas Roy's largest characteristic root is shown to be rather insensitive to alternatives involving more than one non-zero root. Other proposed test statistics are shown to be less sensitive as judged by the ESL criterion.