TREATING BIAS AS VARIANCE FOR EXPERIMENTAL DESIGN PURPOSES

NORMAN R. DRAPER^{1} AND IRWIN GUTTMAN^{2}

1Statistics Department, University of Wisconsin, 1210 West Dayton Street, Madison, WI 53706, U.S.A.

2Statistics Department, University of Toronto, Toronto, Ontario, Canada M5S 1A1

(Received July 1, 1991; revised October 21, 1991)

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.

Key words and phrases: Bias error, experimental design, response surface, variance error.