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An Agronomically Useful Three-Factor Response Surface Design Based on Dodecahedron Symmetry¹

Synopsis: This design allows application of 3 quantitative independent variables at 7 preselected levels each and the fitting of a second degree polynomial to the quantitative dependent variable data. Thirty plots per replicate can be divided into 5 equal sized blocks of 6 plots. An estimate of error with five degrees of freedom is available within each replicate. This design has proven practical for soil fertility field experimentation and an example of this application is given.

² Former Research Assistant (now Assistant Professor and Assistant Agricultural Chemist, University of Idaho), Associate Professor and Agricultural Experiment Station Statistician, former Research Assistant (now employed by Control Data Corporation, Minneapolis, Minn.), and Assistant Professor, respectively. Appreciation is expressed to Bengt Torssell for his constructive criticism during preparation of the manuscript and to A. C. Caldwell and W. P. Martin for their support.