An Analysis of Rectangular Lattices with Unequal Block Sizes, Using Inter-Block Information

Abstract

THE square lattice design (2) and the three-dimensional cubic lattice design (7) are available for variety trials and experiments with large numbers of treatments; both designs permit recovery of inter-block information. Yates (6) has also given the design and analysis of a rectangular lattice for pq varieties, using blocks of unequal sizes, but without recovery of inter-block information. The present paper extends the analysis to recover this information, using the assumption that the inter-block and intra-block components of variance are little affected by the unequal block sizes. In practice p and q need seldom differ by more than one, and when q = p + 1 the rectangular lattice design with blocks of equal size, developed by Harshbarger (4), is preferable, using the method of analysis given by Cochran and Cox (1), (cf. also Grundy, 3). The unequal block design may, however, be useful in some cases where the difference between p and q exceeds unity, but is neither greater than 5 nor greater than 10% of pq.