
Accession Number : AD0638730
Title : SOME EXTENSIONS OF SOMERVILLE'S PROCEDURE FOR RANKING MEANS OF NORMAL POPULATIONS.
Descriptive Note : Technical rept.
Corporate Author : CORNELL UNIV ITHACA N Y DEPT OF INDUSTRIAL ENGINEERING AND OPERATIONS RESEARCH
Personal Author(s) : Fairweather,William R.
Report Date : JUL 1966
Pagination or Media Count : 82
Abstract : In an article in Biometrika Vol. 41 (1954), Somerville proposed a onestage and a twostage procedure (which eliminates one population after the first stage) for selecting the population with the largest mean from a set of normal populations with unknown means and a common, known variance. He assumed that a certain loss was incurred on making an incorrect selection and also assumed a sampling cost. He showed numerically, for the special case of three populations, that the twostage procedure, when using appropriate allocations of observations between stages, has a smaller maximum expected loss (maximum over the possible configuration of the true population means) than does the onestage procedure. In this paper the formulation of Somerville's twostage procedure is extended to arbitrary numbers of populations, and the procedures are studied numerically for the case of four populations. For this case, two 2stage procedures are possible (eliminating either one or two populations after the first stage) and it is found that both twostage procedures, using appropriate allocations, have smaller maximum expected losses than does the corresponding onestage procedure, but which twostage procedure is the better depends on the allocation. Methods of extending the formulation to multistage procedures are also considered. Numerical studies, which are undertaken require the evaluation of 5 variate normal integrals with arbitrary correlation coefficients and limits of integration. This is accomplished using a method suggested by Plackett in Biometrika Vol. 41 (1954). (Author)
Descriptors : (*STATISTICAL ANALYSIS, SEQUENTIAL ANALYSIS), SAMPLING, DECISION THEORY, OPTIMIZATION
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE