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    Optimal and efficient crossover designs for comparing test treatments with a control treatment

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    This paper deals exclusively with crossover designs for the purpose of comparing t test treatments with a control treatment when the number of periods is no larger than t+1. Among other results it specifies sufficient conditions for a crossover design to be simultaneously A-optimal and MV-optimal in a very large and appealing class of crossover designs. It is expected that these optimal designs are highly efficient in the entire class of crossover designs. Some computationally useful tools are given and used to build assorted small optimal and efficient crossover designs. The model robustness of these newly discovered crossover designs is discussed.Comment: Published at http://dx.doi.org/10.1214/009053604000000887 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

    A generalization of sum composition: Self orthogonal Latin square design with sub self orthogonal Latin square designs

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    AbstractA generalization of the theory of sum composition of Latin square designs is given. Via this generalized theory it is shown that a self orthogonal Latin square design of order (3pα − 1)2 with a subself orthogonal Latin square design of order (pα − 1)2 can be constructed for any prime p > 2 and any positive integer α as long as p ≠ 3, 5, 7 and 13 if α = 1. Additional results concerning sets of orthogonal Latin square designs are also provided
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