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A Two-Stage Selection and Testing Design for Comparing Several Normal Means with a Standard: The Case of Common, Known Variance

机译：两种标准均值比较的两阶段选择和测试设计：常见，已知方差的情况

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摘要

A two-stage design is proposed for the goal of selecting one among k experimental treatments, provided that it is better than a specified standard. In the first stage, ranking and selection techniques are used to screen out the one most promising treatment. In the second stage, hypothesis testing techniques are used to determine if the treatment chosen in the first stage is better than the standard. The design allows for early termination of the procedure at stage one if none of the treatments seem promising. All the treatments are assumed to follow normal distributions with a common known variance. A large population mean is assumed to be desirable, and hence "better than the standard" means that the population mean is sufficiently larger than the standard. Appropriate definitions of size and power are given. Tables of procedure parameters for achieving desired size and power are provided. Sample size requirements arc compared with the single-stage procedure of Bechhofer and Turnbull (Bechhofcr, R.E.; Turnbull, B.W. Two (k + 1)-dccision selection procedures for comparing k normal means with a specified standard. Journal of the American Statistical Association 1978, 73, 385 392).
机译：提出了一个两阶段设计，目的是在k种实验处理方法中选择一种，前提是要优于指定的标准。在第一阶段，使用排名和选择技术来筛选出最有希望的治疗方法。在第二阶段中，使用假设检验技术来确定在第一阶段中选择的治疗是否优于标准治疗。如果没有一种治疗方法有希望，则该设计允许在第一阶段尽早终止手术。假定所有处理均遵循正态分布，并具有共同的已知方差。假定较大的总体平均值是理想的，因此“优于标准”表示总体平均值充分大于标准。给出了尺寸和功率的适当定义。提供了用于实现所需大小和功率的过程参数表。与Bechhofer和Turnbull（Bechhofcr，RE; Turnbull，BW）的单阶段程序相比，样本量要求两个样本（k + 1）的选择程序，用于将k均值与指定标准进行比较。美国统计协会，1978年，73，385392）。

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