Relative Efficiency of Rectangular and Triple Rectangular Lattice Designs Using Hop Uniformity Trial Data 1

TVTUMEROUS investigations have been reported -L^l concerning the efficiency of incomplete block designs relative to randomized complete blocks. These investigations have been limited, in general, to cereal crops involving a large number of entries where the use of incomplete block designs has usually resulted in a gain in efficiency. Greater gains in efficiency have been reported on heterogeneous soils. These studies, in addition, have been confined to experimental designs in which the total number of entries in an experimental trial is equal to the square of a number. Incomplete block designs which are limited to k entries, where k equals the number of plots in an incomplete block, are widely used by investigators working with annual crops. An objection to the restriction of k entries is that it often necessitates including in the experiment a number of "filler" varieties to complete the square. This difficulty is of more importance where perennial plants are involved, since these experimental trials are usually conducted for several years on the same site. The solution for the analysis of the rectangular lattice (3) and the triple rectangular lattice designs (4) presents an extension of the incomplete block design to the case when the number of entries is expressible as the product of two consecutive integers. The introduction of the rectangular and triple rectangular lattice designs provides the investigator with additional incomplete block designs which may reduce the number of "filler" entries to complete the experiment. The objective of this investigation was to examine the efficiency of rectangular and triple rectangular