## The Annals of Mathematical Statistics

### A Single-Sample Multiple Decision Procedure for Ranking Means of Normal Populations with known Variances

Robert E. Bechhofer

#### Abstract

This paper is concerned with a single-sample multiple decision procedure for ranking means of normal populations with known variances. Problems which conventionally are handled by the analysis of variance (Model I) which tests the hypothesis that $k$ means are equal are reformulated as multiple decision procedures involving rankings. It is shown how to design experiments so that useful statements can be made concerning these rankings on the basis of a predetermined number of independent observations taken from each population. The number of observations required is determined by the desired probability of a correct ranking when certain differences between population means are specified.

#### Article information

Source
Ann. Math. Statist. Volume 25, Number 1 (1954), 16-39.

Dates
First available in Project Euclid: 28 April 2007

https://projecteuclid.org/euclid.aoms/1177728845

Digital Object Identifier
doi:10.1214/aoms/1177728845

Mathematical Reviews number (MathSciNet)
MR60197

Zentralblatt MATH identifier
0055.13003

JSTOR