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 one-stage and a two-stage 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 two-stage 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 one-stage procedure. In this paper the formulation of Somerville's two-stage procedure is extended to arbitrary numbers of populations, and the procedures are studied numerically for the case of four populations. For this case, two 2-stage procedures are possible (eliminating either one or two populations after the first stage) and it is found that both two-stage procedures, using appropriate allocations, have smaller maximum expected losses than does the corresponding one-stage procedure, but which two-stage procedure is the better depends on the allocation. Methods of extending the formulation to multi-stage 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