Some Considerations in the Optimal Design of Experiments in Non-Optimal Situations

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1976 · Volume 38 · Issue 3

DOI: 10.1111/j.2517-6161.1976.tb01596.x

Abstract

Designs which satisfy optimal design criteria will usually not be optimal when some observations are missing, when outliers are present or when, contrary to the assumptions, the error of the observations arises from a non-Gaussian distribution. Designs robust against such short-comings will be introduced. They are slightly less than optimal under ideal conditions but will be more efficient under more realistic conditions. The probability of breakdown of a design is defined. Measures of robustness of a design are introduced in the cases of the generalized variance and the minimization of the maximum variance criteria. These measures and the probability of breakdown should be taken into account when the decision for a particular type of design is made. Some examples are given.

Keywords

experimental design, robustness, optimal design, missing values, outliers, non-gaussian distributions

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