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An Investigation of Some of the Relationships between Copper, Iron, and Molybdenum in the Growth and Nutrition of Lettuce: I. Experimental Design and Statistical Methods for Characterizing the Response Surface^{1, 2,}

ABSTRACT

In studies involving the experimental determination of critical levels of plant nutrients and optimum rates of fertilizer application, the need for the consideration of joint effects of other nutrients has long been realized. Where such joint effects or interactions exist, characterization of the response surface is essential for the realistic evaluation of the responses. The use of the complete factorial experiment provides a means of estimating the response surface; but the number of treatment combinations required, especially where more than two nutrients or factors are involved, has often prohibited their use in field and greenhouse research.

Where a polynomial model may be used to approximate a response surface, new experimental designs, known as the composite and rotatable designs, have been developed by Box and Hunter. In these designs, the treatment combinations are selected to allow estimation of the parameters of the model. These designs use considerably fewer treatment combinations for the experiment than required by the complete factorial arrangement. Other important advantages of those designs are discussed.

The basis of construction of these designs is briefly discussed and some examples are presented. The details of statistical analysis are illustrated by the use of experimental data from a greenhouse experiment with lettuce.

¹ Joint contribution from Department of Agronomy and Department of Statistics, North Carolina Agr. Exp. Sta., Raleigh, North Carolina. Submitted with the approval of the Director as paper No. 651 of the Journal Series. Presented before Div. IV, Soil Science Society of America, Davis, Calif., Aug. 17, 1955.

² Statistical aspects partially sponsored by the Office of Ordnance Research.

³ Associate Professor of Experimental Statistics; formerly Research Assistant Professor of Agronomy, now Assistant Professor of Soils, Oregon State College; Professor of Experimental Statistics; and formerly Graduate Assistant, N. C. State College, now Graduate Assistant, University of California, respectively.

Received for publication August 20, 1955. Accepted for publication May 14, 1956.