Open Access
June 1996 Optimal blocked main effects plans with nested rows and columns and related designs
J. P. Morgan, Nizam Uddin
Ann. Statist. 24(3): 1185-1208 (June 1996). DOI: 10.1214/aos/1032526963


Optimal design is studied for factorial experiments in the nested row and column setting. The approach is analogous to that of orthogonal Latin squares: main effects plans are found by the superimposition of one nested row and column design upon another. Conditions are stated for statistical orthogonality of the superimposed components, resulting in orthogonal main effects plans, and a number of constructions are given. Orthogonal collections of sets of Latin squares are introduced. All of the constructed designs are also optimal main effects plans for the row-column and the unstructured block design settings. Further applications are as optimal multidimensional incomplete block designs and as optimal designs for multistage experimentation.


Download Citation

J. P. Morgan. Nizam Uddin. "Optimal blocked main effects plans with nested rows and columns and related designs." Ann. Statist. 24 (3) 1185 - 1208, June 1996.


Published: June 1996
First available in Project Euclid: 20 September 2002

zbMATH: 0862.62065
MathSciNet: MR1401844
Digital Object Identifier: 10.1214/aos/1032526963

Primary: 62K05 , 62K15
Secondary: 62K10 , 62K99

Keywords: Balanced incomplete block design , bottom-stratum universally optimal nested row and column design , Latin square , optimal design , orthogonality , Youden design

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 3 • June 1996
Back to Top