Sensitivity Comparisons among Tests of the General Linear Hypothesis
作者:
Martin Schatzoff,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1966)
卷期:
Volume 61,
issue 314
页码: 415-435
ISSN:0162-1459
年代: 1966
DOI:10.1080/01621459.1966.10480878
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
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 hypothesisH0:X∼F(x) againstH1:X∼G(x) is given by ñF(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'sT02provide 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.
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