Relative Efficiency of Factorial Designs for Estimating Response Surfaces with Reference to Gaseous Pollutant Mixtures

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Abstract
The evaluation of the effects of air pollutant mixtures on plant growth is very demanding of experimental resources since each replicate of each pollutant treatment requires a separate chamber. Consequently the choice of an efficient experimental design is particularly important. In 1954 Box was the first researcher to recognize that when all factors are quantitative, complete factorial designs are often inefficient. He proposed using a class of incomplete factorial designs termed response surface designs. This paper presents the statistical methodology for comparing experimental designs and illustrates this methodology by comparing five commonly used two factor designs—three response surface designs and two complete factorial designs. The response surface designs were the most efficient. However, failure to replicate the center point as recommended will dramatically reduce efficiency of the design near the center. Placement of treatments outside the region of interest can increase precision within the region of interest, particularly near the boundary. The methodology that is presented may be used for comparing designs with any number of factors.
Funding Information
  • Natural Sciences and Engineering Research Council of Canada

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