The superposition of t treatments on a (t - 1) × t Youden square design

Abstract

Representative members of the species of (t - 1) × t Youden squares for t = 4, 5, 6 are given. The superposition of a further set of t non-interacting treatments on such a design leads to an O: OT: OTT design. The numbers of O: OT: OTT designs for each species of Youden squares are given, together with examples of the various types of solution where they exist. For 3 × 4 Youden squares there are O: OT: OTT solutions for both species, but for 4 × 5 Youden squares there is a solution for only one of the three species. For 5 × 6 Youden squares the numbers of O: OT: OTT solutions for the 33 species ranges from 0 to 160.