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Biometrika 2002 89(4):877-891; doi:10.1093/biomet/89.4.877
© 2002 by Biometrika Trust
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Generalised incomplete Trojan designs

R.N. Edmondson1

1 Horticulture Research International, Wellesbourne, Warwick CV 35 9L S, U.Krodney.edmondson{at}hri.ac.uk

Generalised incomplete (m x n)/k Trojan designs for m replicates of nk treatments based on sets of k cyclic generators are discussed. Normal equations for plots-within-columns, plots-within-blocks and blocks-within-columns treatment effects are developed.The nk treatments are divided into k subsets each of size n and the conditional plots-within-blocks and blocks-within-columns information matrix for each subset is defined. Efficient conditional treatment estimates are discussed and efficient generators for the various strata are discussed. Balanced (m x n)/k incomplete Trojan designs based on Youden generators are constructed and designs based on multiples of a single generator are discussed. Some ideas for constructing efficient general (m x n)/2 designs are outlined and some advantages of generalised incomplete Trojan designs are discussed.

Key Words: Agricultural experiment; Cyclic design; Incomplete Trojan square; Latinised block; Row-and-column design; Semi-Latin square

Received March 2001. Revised February 2002


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