An analysis of three-level orthogonal saturated designs

Although three-level factorial designs with quantitative factors are not the most efficient way to fit a second-order polynomial model, they often find some application, when the factors are qualitative. The three-level orthogonal designs with qualitative factors are frequently used, e.g., in agriculture, in clinical trials and in parameter designs. It is practically unavoidable that, because of the limitation of experimental materials or time-related constraint, we often have to keep the number of experiments as small as possible and to consider the effects of many factors and interactions simultaneously so that most of such designs are saturated or nearly saturated. An experimental design is said to be saturated, if all degrees of freedom are consumed by the estimation of parameters in modelling mean response. The difficulty of analyzing orthogonal saturated designs is that there are no degrees of freedom left to estimate the error variance so that the ordinary ANOVA is no longer available. In this paper, we present a new formal test, which is based on mean squares, for analyzing three-level orthogonal saturated designs. This proposed method is compared via simulation with several mean squares based methods published in the literature. The results show that the new method is more powerful in terms of empirical power of the test. Critical values used in the proposed procedure for some three-level saturated designs are tabulated. Industrial examples are also included for illustrations.Saturated design Unreplicated factorial Mean square Formal test Interaction