Experimental design is concerned with the allocation of treatments to units. The methods of optimum design were originally developed for the choice of those values of the explanatory variables x in a regression model at which observations should be taken (Smith 1918). For example, in a chemical experiment there may be several factors, such as time of reaction, temperature, pressure and catalyst concentration, that affect the response which is a smooth function of these variables (see Response Surface Methodology). At what combination of variables should measurements be taken in order to obtain good estimates of the dependence of responses, such as yield or purity of product, on these variables? More recent developments include the design of experiments for the nonlinear models occurring in pharmacokinetic experiments in drug development (Gagnon 2005).
Perhaps after data transformation (see Box-Cox Transformations), efficient analysis of regression experiments requires the use of least...
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References and Further Reading
Atkinson AC, Donev AN, and Tobias RD (2007) Optimum experimental designs, with SAS. Oxford University Press, Oxford
Brown LD, Olkin I, Sacks J, Wynn HP (eds) (1985) Jack Carl Kiefer collected papers III. Wiley, New York
Fedorov VV, Hackl P (1997) Model-oriented design of experiments. Lecture Notes in Statistics 125. Springer, New York
Gagnon RC, Leonov SL (2005) Optimum population designs for PK models with serial sampling. J Biopharm Stat 15:143–163
Kiefer and Wolfowitz J (1960) The equivalence of two extremum problems. Canadian J Math 12:363–366
Smith K (1918) On the standard deviations of adjusted and interpolated values of an observed polynomial function and its constants and the guidance they give towards a proper choice of the distribution of observations. Biometrika 12:1–85
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Atkinson, A.C. (2011). Optimum Experimental Design. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_434
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