TESTING WHETHER AN IDENTIFIED TREATMENT IS BEST
TESTING WHETHER AN IDENTIFIED TREATMENT IS BEST
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DOI：
10.2307/2531766
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发表时间：
1989-12-01
期刊：
影响因子：
1.9
通讯作者：
MEISNER, MJ
中科院分区：
文献类型：
--
作者：
LASKA, EM;MEISNER, MJ
我们考虑了检验确定的处理是否比K处理中的每一个处理更好的问题。假设存在单变量检验统计量Si，其将所识别的处理与i=1，2，k的处理i进行比较。最小检验被定义为当对于所有i，Si拒绝所识别的处理不比第i个处理更好的片面假设时，最小检验被定义为拒绝所识别的处理不是最好的零假设的α水平过程。在Si为t统计量的正常情况下，最小检验是似然比检验。对于满足温和正则性条件的分布，如果将注意力限制在作为Si的单调非递减函数的检验统计量上，则无论其协方差结构如何，最小检验都是最优α水平检验。给出了当Si为学生‘’S t和Wilcoxon‘’时，实现幂.5、.8、.90和.95所需样本量的表格。
We consider the problem of testing whether an identified treatment is better than each of K treatments. Suppose there are univariate test statistics Si that contrast the identified treatment with treatment i for i = 1,2...,K. The min test is defined to be the .alpha.-level procedure that rejects the null hypothesis that the identified is not best when, for all i, Si rejects the one-sided hypothesis, at the .alpha.-level, that the identified treatment is not better than the ith treatment. In the normal case where Si are t statistics the min test is the likelihood ratio test. For distributions satisfying mild regularity conditions, if attention is restricted to test statistics that are monotone nondecreasing functions of Si, then regardless of their covariance structure the min test is an optimal .alpha.-level test. Tables of the sample size needed to achieve power .5, .8, .90, and .95 are given for the min test when the Si are Student''s t and Wilcoxon.