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Optimal Rotations to Balance Sequential Effects

Russ, W., Yang, K., and Ennis, D. (2023). IFPress, 26(3) 5-6.



In previous technical reports we discussed methods for developing improved rotations for sequential testing to remove bias and lower testing variances. The benefit of doing this is to obtain more accurate information and to create more powerful tests with the opportunity to lower testing cost. For most designs, the use of the Column Randomization and Search (CRAS)1 method has proven to be useful for many designs including complete block, incomplete block, and testing with sequences containing interruptions, such as testing over several days. This method searches for position, sequences and the location of sequences in the design (called sequence spread) that are not often accounted for in the experimental design of product tests, other types of surveys and clinical trials. When they are considered, it is common to use Williams Squares to control for position and sequences but not sequence spread. For instance, if the sequence (1 2) occurs at the beginning and end of a Williams Square with multiple products, this sequence will never occur at the middle of the test and replication will perpetuate this condition. This could be important because performance from the beginning to the end of a series of evaluations changes and could be different for the sequences as well as the products themselves. These designs are replicated when the number of rotations needed exceeds the size of the design. It is possible to overcome this limitation of replicated Williams Squares so that designs based on them can handle sequence spread. The purpose of this technical report is to explore this possibility.

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