A Class of Experimental Designs Using Blocks of Two Plots

Abstract

Over the past fifteen or so years, a large number of classes of experimental designs have been evolved by Yates, Bose and Nair and others (see [1] for a systematic account). The aim in all cases was to evolve patterns of observation which could utilize natural groupings in the experimental material, such as for instance litters of mice or small numbers of plots perhaps contiguous to each other. By arranging the treatments to be compared in specific ways which utilize the natural grouping, it is possible to enable treatment contrasts to be estimated by comparisons of observations on experimental units, which we shall call plots, within the natural groups. This enables the comparisons to be made usually with considerably greater accuracy than would obtain if the experimenter were forced to randomize the positions of the treatments without respect to these groupings. In experimental work in some branches of biology, natural groups of size two are of fairly frequent occurrence, for example twins, or halves of plants, or halves of leaves. The development of experimental designs is not complete in this particular respect. The designs which have been developed for blocks of two plots or experimental units are as follows: (1) symmetrical pairs (Yates, [2]) which require $(t - 1)$ replicates if there are $t$ treatments. (2) quasifactorial designs if the number of treatments is a power of 2 (see [1] in this respect). It appears therefore that development of a class of designs using blocks of two plots is desirable, and this is the purpose of the present paper.