## The Annals of Mathematical Statistics

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

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

#### 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: 28 April 2007

**Permanent link to this document**

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

**JSTOR**

links.jstor.org

**Digital Object Identifier**

doi:10.1214/aoms/1177728845

**Mathematical Reviews number (MathSciNet)**

MR60197

**Zentralblatt MATH identifier**

0055.13003

#### Citation

Bechhofer, Robert E. A Single-Sample Multiple Decision Procedure for Ranking Means of Normal Populations with known Variances. The Annals of Mathematical Statistics 25 (1954), no. 1, 16--39. doi:10.1214/aoms/1177728845. http://projecteuclid.org/euclid.aoms/1177728845.