Abstract
When an empirical model is fitted to data, bias can arise from terms that have not been incorporated, and this can have an important effect on the choice of an experimental design. Here, the biases are treated as random, and the consequences of this action are explored for the fitting of models of first and second order.
Similar content being viewed by others
References
Bandemer, H., Näther, W. and Pilz, J. (1987). Once more: optimal experimental design for regression models (with discussion), Statistics, 18, 171–217.
Box, G. E. P. and Draper, N. R. (1959). A basis for the selection of a response surface design, J. Amer. Statist. Assoc., 54, 622–654.
Box, G. E. P. and Draper, N. R. (1963). The choice of a second order rotatable design, Biometrika, 50, 335–352.
Bunke, H. and Bunke, O. (1986). Statistical Inference in Linear Models, Wiley, New York.
Draper, N. R. and Guttman, I. (1986). Response surface designs in flexible regions, J. Amer. Statist. Assoc., 81, 1089–1094.
Draper, N. R. and Lawrence, W. E. (1965a). Designs which minimize model inadequacies; cuboidal regions of interest, Biometrika, 52, 111–118.
Draper, N. R. and Lawrence, W. E. (1965b). Mixtures designs for three factors, J. Roy. Statist. Soc. Ser. B, 27, 450–465.
Draper, N. R. and Lawrence, W. E. (1966). The use of second-order “spherical” and “cuboidal” designs in the wrong regions, Biometrika, 53, 596–599.
Draper, N. R. and Lawrence, W. E. (1967). Sequential designs for spherical weight functions, Technometrics, 9, 517–529.
Kiefer, J. (1985). Collected Papers III, Design of Experiments, Springer, New York.
Steinberg, D. M. (1985). Model robust response surface designs: scaling two-level factorials, Biometrika, 72, 513–526.
Welch, W. J. (1983). A mean squared error criterion for the design of experiments, Biometrika, 70, 205–213.
Author information
Authors and Affiliations
About this article
Cite this article
Draper, N.R., Guttman, I. Treating bias as variance for experimental design purposes. Ann Inst Stat Math 44, 659–671 (1992). https://doi.org/10.1007/BF00053396
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00053396