A two-stage procedure on comparing several experimental treatments and a control—the common and unknown variance case. Issue 1 (26th April 2005)

• Record Type: Journal Article
• Authors: Zhang, John; Chen, Pinyuen; Fang, Yue
• Is Part Of: Journal of applied mathematics & decision sciences. Volume 2005:Issue 1(2005)
• Page Start: 47
• Page End: 58
• Publication Date: 2005-04-26
• Subjects: Operations research -- Periodicals; Mathematical models -- Periodicals; Statistics -- Periodicals; Quality control -- Periodicals; Mathematical models; Operations research; Quality control; Statistics; Periodicals; 519.05
• DOI: 10.1155/JAMDS.2005.47
• Languages: English
• ISSNs: 1173-9126

Abstract

Abstract : This paper introduces a two-stage selection rule to compare several experimental treatments with a control when the variances are common and unknown. The selection rule integrates the indifference zone approach and the subset selection approach in multiple-decision theory. Two mutually exclusive subsets of the parameter space are defined, one is called the preference zone (PZ) and the other, the indifference zone (IZ). The best experimental treatment is defined to be the experimental treatment with the largest population mean. The selection procedure opts to select only the experimental treatment which corresponds to the largest sample mean when the parameters are in the PZ, and selects a subset of the experimental treatments and the control when the parameters fall in the IZ. The concept of a correct decision is defined differently in these two zones. A correct decision in the preference zone (CD 1 ) is defined to be the event that the best experimental treatment is selected. In the indifference zone, a selection is called correct (CD 2 ) if the selected subset contains the best experimental treatment. Theoretical results on the lower bounds forP ( CD 1 ) in PZ andP ( CD 2 ) in IZ are developed. A table is computed for the implementation of the selection procedure.