Optimal row–column design for three treatments

The A-optimality problem is solved for three treatments in a row–column layout. Depending on the numbers of rows and columns, the requirements for optimality can be decidedly counterintuitive: replication numbers need not be as equal as possible, and trace of the information matrix need not be maxim...

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Bibliographic Details
Published inJournal of statistical planning and inference Vol. 137; no. 4; pp. 1474 - 1487
Main Authors Morgan, J.P., Parvu, Valentin
Format Journal Article
LanguageEnglish
Published Lausanne Elsevier B.V 01.04.2007
New York,NY Elsevier Science
Amsterdam
Subjects
A-optimality
Combinatorics
Combinatorics. Ordered structures
Designs and configurations
Exact sciences and technology
Experimental design
General topics
Mathematics
Probability and statistics
Row–column blocking
Sciences and techniques of general use
Statistics
Sufficiency and information
Uniform treatment assignment
Uniform treatment assignment
Row–column blocking
A-optimality
Statistical method
Information measure
Row column design
Block design
Experimental design
Row-column blocking
Statistical decision
Optimal design(statistics)
Information matrix
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Summary:The A-optimality problem is solved for three treatments in a row–column layout. Depending on the numbers of rows and columns, the requirements for optimality can be decidedly counterintuitive: replication numbers need not be as equal as possible, and trace of the information matrix need not be maximal. General rules for comparing 3 × 3 information matrices for their A-behavior are also developed, and the A-optimality problem is also solved for three treatments in simple block designs.
ISSN:0378-3758
1873-1171
DOI:10.1016/j.jspi.2006.02.006