Augmented Designs with One-Way Elimination of Heterogeneity

Abstract

One of the principal problems in plant breeding and in biochemical research of new pesticides, herbicides, soil fumigants, drugs, etc., is the evaluation of the new strain or chemical. Efficient experimental designs and efficient screening procedures are necessary in order to make the most efficient use of available resources. In some instances sufficient material of a new strain or a new chemical is available for only one or two observations (plots). Hence, the experimenter should use an experimental design and a screening procedure suitable for these conditions. In other cases, the experimenter may wish to limit his observations to a single observation on the new material. In still other cases (e.g., in physics), a single observation on new material may be desirable because of relatively low variability in the experimental material. Furthermore, it may be desired to combine screening experiments on new material and preliminary testing experiments on promising material. The experimental design should be selected to meet the requirements of such experiments rather than selecting the material and experiments to meet the requirements of the experimental design. The experimnental designs described in the present paper were developed to satisfy requirements such as those described above. The class of experimental designs known as augmented designs was Introduced by the author in 1955 to fill a need arising in screening new strains of sugar cane and soil fumigants used in growing pineapples2 (Federer [1956a, 1956b, 1956c, 1958]). An augmented experimental design is any standard design augmented with additional treatments in the complete block, the incomplete block, the row, the column, etc.