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Biometrika 2002 89(1):225-229; doi:10.1093/biomet/89.1.225
© 2002 by Biometrika Trust
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Miscellaneous

Optimal main effect plans with non-orthogonal blocking

Rahul Mukerjee1, Aloke Dey2 and Kashinath Chatterjee3

1 Indian Institute of Management, P.O.Box 16757, Calcutta 700 027, India rmuk1{at}hotmail.com 2 Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, New Delhi 110 016, India adey{at}isid.ac.in 3 Department of Statistics, Asutosh College, 92 S.P. Mukherjee Road, Calcutta 700 026, India kashi{at}cal2.vsnl.net.in

The current literature on fractional factorial plans in block designs centres around orthogonal blocking which may not, however, always be attainable because of practical restrictions on the block size.For general factorials, including asymmetric ones, sufficient conditions are indicated in this paper for a main effect plan to be universally optimal under possibly non-orthogonal blocking. A construction procedure is given using generalised Youden designs in conjunction with orthogonal arrays. We also illustrate how the procedure can be applied to obtain optimal main effect plans in the practically important situation where each factor has two or three levels and the block size is small.

Key Words: Adding column technique; Generalised Youden design; Orthogonal array; Paired comparison design; Universal optimality

Received February 2001


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