## The Annals of Mathematical Statistics

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

V. L. Mote

#### 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

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