Four-Way Balanced Designs Based on Youden Squares with 5, 6, or 7 Treatments

Abstract

Details are given of how to construct 0: OT TOO designs in which a second set of treatments is superimposed on a 5 X 4 or a 6 X 5 Youden square, using as a basis Fisher and Yates's [1963] list of standard 5 X 5 and 6 X 6 Latin squares. For 6 X 5 designs, six different patterns of occurrence have arisen for the second set of treatments. The existence of 7 X 4 designs of this type is also demonstrated, and the form of analysis given.