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September, 1958 On a Minimax Property of a Balanced Incomplete Block Design
V. L. Mote
Ann. Math. Statist. 29(3): 910-914 (September, 1958). DOI: 10.1214/aoms/1177706550


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.


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V. L. Mote. "On a Minimax Property of a Balanced Incomplete Block Design." Ann. Math. Statist. 29 (3) 910 - 914, September, 1958.


Published: September, 1958
First available in Project Euclid: 27 April 2007

zbMATH: 0099.13601
MathSciNet: MR98453
Digital Object Identifier: 10.1214/aoms/1177706550

Rights: Copyright © 1958 Institute of Mathematical Statistics

Vol.29 • No. 3 • September, 1958
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