Optimal Rotations for Incomplete Designs

Ennis, D. M. and Rousseau, B. (2021). IFPress, 24(3) 3-4.



Designs for sequential monadic consumer product research, whether complete or incomplete, are subject to compromise due to attrition during testing. So, no matter how perfectly balanced a design may be at the outset, the final data will inevitably reflect a deviation from perfection. In previous technical reports, we have discussed different approaches to accounting for position, sequential effects and sequence spread in sequential monadic (complete block) designs and argue for rotations that minimize the impact of these variables at the outset of testing so that their effects on bias and variance in the final analyses can be minimized. Note that minimizing these effects is essential whether one expects attrition to be an issue or not. We recommended the use of Column Randomization and Search (CR&S) to create optimal rotations and showed how this approach is superior to either within subject randomization or replicated Williams Squares. CR&S is a computer intensive method that considers millions of possible designs and chooses a design that minimizes the variances in the counts of products by position, by paired sequences, and by sequence spread throughout the design. In this technical report we explore rotations for incomplete designs.