Designs for Sequences of Treatments with Carry-Over Effects

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Abstract
In experimental situations where treatments are applied in sequence to the same experimental units and the effect of a treatment may persist after a treatment has been discontinued, the experimenter may be more interested in the effect of consecutive applications of a treatment rather than in the direct and carry-over effects. Designs are presented in which the effect of a sequence of treatments is the quantity to be estimated. Attention is limited to designs containing all possible sequences of a given length n consisting of consecutive applications of a single treatment or of r applications of one treatment followed by n - r applications of a 2nd treatment. Designs are presented for treatments in incomplete blocks, of size 2, within experimental units and for treatments in complete blocks within experimental units. General analyses are given to the incomplete block design and for the complete block design when the number of treatments is even.

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