A SEQUENTIAL MULTIPLE-DECISION PROCEDURE FOR SELECTING THE BEST ONE OF SEVERAL NORMAL POPULATIONS WITH A COMMON UNKNOWN VARIANCE, AND ITS USE WITH VARIOUS EXPERIMENTAL DESIGNS
A SEQUENTIAL MULTIPLE-DECISION PROCEDURE FOR SELECTING THE BEST ONE OF SEVERAL NORMAL POPULATIONS WITH A COMMON UNKNOWN VARIANCE, AND ITS USE WITH VARIOUS EXPERIMENTAL DESIGNS
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DOI：
10.2307/2527883
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发表时间：
1958-01-01
期刊：
影响因子：
1.9
通讯作者：
BECHHOFER, RE
中科院分区：
文献类型：
--
作者：
BECHHOFER, RE
所描述的过程是先前提出的在已知共同方差的情况下处理相同问题的过程的推广。这两个过程都以概率统一结束，并保证当最大总体均值大于第二维均值时，正确选择的概率至少等于某个指定的概率。对于任何给定的总体均值配置，实验结束所需的平均样本量随着实验基础的总体方差的减小而减小。因此，使用有效地减少这种潜在方差的实验设计将导致终止所需的平均样本量的减少。平均样本量也随着总体均值的配置变得更有利而减小。描述了将该方法应用于各种实验设计的方法。还给出了计算量比精确方法少得多的近似方法。给出了一个算例。
The procedure described is a generalization of one which was previously proposed to handle the same problem when the common variance is known. Both procedures terminate with probability unity and guarantee that the probability of a correct selection is at least equal to some specified probability whenever the largest population mean is greater than the 2d-largest by some specified amount. For any given configuration of the population means, the average sample size required for termination of experimentation decreases as the population variance underlying the experiment decreases. Hence, the use of an experimental design which is effective in cutting down on this underlying variance will result in a decrease in the average sample size required for termination. The average sample size also decreases as the configuration of the population means becomes more favorable. The method of applying the procedure with various experimental designs is described. Approximate methods involving substantially less computation than the exact method are also given. A worked-out numerical example is provided.