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December, 1970 The Optimum Design of a Two-Factor Experiment Using Prior Information
R. J. Owen
Ann. Math. Statist. 41(6): 1917-1934 (December, 1970). DOI: 10.1214/aoms/1177696693


This paper is concerned with a two-factor analysis of variance situation, the factors being conveniently referred to as blocks and treatments. One of the treatments has the role of a control. Attention is focused on inference about the treatment parameters, the block parameters being regarded as nuisance parameters. With a general multivariate normal form for the distribution of errors and for the prior distribution on the block and treatment parameters, the posterior distribution of the treatment parameters is derived. With a quadratic loss function an algorithm is derived for the optimum allocation of treatments over a given sample with known blocking. In special cases the optimum allocation can be written down immediately and the algorithm need not be resorted to.


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R. J. Owen. "The Optimum Design of a Two-Factor Experiment Using Prior Information." Ann. Math. Statist. 41 (6) 1917 - 1934, December, 1970.


Published: December, 1970
First available in Project Euclid: 27 April 2007

zbMATH: 0215.26602
MathSciNet: MR279943
Digital Object Identifier: 10.1214/aoms/1177696693

Rights: Copyright © 1970 Institute of Mathematical Statistics

Vol.41 • No. 6 • December, 1970
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