BIAS OF EXPERIMENTAL DESIGNS WITH NULL ODD MOMENTS

Abstract

Statistical research in relation to bias of experimental designs, has been mainly concentrated on first and second order designs, when it is assumed that the true answers are second and third order functions, respectively. In essence it has been attempted to minimize bias, as well as to provide criteria to select designs which generate estimators of minimum bias. However, the direct determination of bias with the purpose of characterizing experimental designs, has not been attempted. In this work we determine the bias of those designs, for which the odd moments, pure or mixed, are cancelled when a second order model is fitted, the true response being a third order function. For these designs, the regression coefficients estimating linear effects, are biased. Such biases have been determined for central composite, 3p factorials, double squares, double cubes, and Plan Puebla designs.