## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 29, Number 3 (1958), 910-914.

### On a Minimax Property of a Balanced Incomplete Block Design

#### Abstract

It is shown that for a given set of parameters ($b$ blocks, $k$ plots per block and $v$ treatments), among the class of connected incomplete block designs, a balanced incomplete block design (if it exists) is the design which maximizes the minimum efficiency, efficiency being defined as $$\frac{\text {Variance of an estimated treatment contrast in a randomized block}{Variance of the estimated treatment contrast in the incomplete block}}.$$ The proof will be preceded by a lemma.

#### Article information

**Source**

Ann. Math. Statist. Volume 29, Number 3 (1958), 910-914.

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

http://projecteuclid.org/euclid.aoms/1177706550

**Digital Object Identifier**

doi:10.1214/aoms/1177706550

**Mathematical Reviews number (MathSciNet)**

MR98453

**Zentralblatt MATH identifier**

0099.13601

**JSTOR**

links.jstor.org

#### Citation

Mote, V. L. On a Minimax Property of a Balanced Incomplete Block Design. Ann. Math. Statist. 29 (1958), no. 3, 910--914. doi:10.1214/aoms/1177706550. http://projecteuclid.org/euclid.aoms/1177706550.