A Second Set of Treatments in a Youden Square Design

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Abstract
A Youden square of size s x (s - 1) may have a second set of treatments superimposed which is orthogonal to the first set and to the columns of the design, and is totally balanced with respect to the rows of the design. Such designs may be constructed whenever an orthogonal (s - 1) x (s - 1) square exists, and are of good efficiency. Analysis is relatively simple because the two non-orthogonalities (first treatments to columns; second treatments to rows) are independent of each other.

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