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On Choosing Among Several Experimental Treatments and a Control
Author(s) -
Chen Pinyuen
Publication year - 1994
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710360610
Subject(s) - monotonic function , selection (genetic algorithm) , mathematics , mathematical optimization , statistics , computer science , artificial intelligence , mathematical analysis
The two classical selection approaches in comparing experimental treatments with a control are combined to form an integrated approach. In this integrated approach, there is a preference zone (PZ) and an indifference zone (IZ), and the concept of a correct decision (CD) is defined differently in each of these zones. In the PZ, we are required to select the best treatment for a correct decision (CD 1 ) but in the IZ, we define any selected subset to be correct (CD 2 ) if it contains the best treatment among all the experimental treatments and the controlled treatment. We propose a single‐stage procedure R to achieve the selection goals CD 1 and CD 2 simultaneously with certain probability requirements. It is shown that both the probability of a correct decision under PZ, P (CD 1 | PZ), and the probability of a correct decision under IZ, P (CD 2 | IZ), satisfy some monotonicity properties and the least favorable configuration in PZ and the worst configuration in IZ are derived by these properties. We also derive formulas for the probabilities of correct decision and provide a brief table to illustrate the magnitude of the procedure parameters and the common sample sizes needed for various probability requirements and configurations.