A supersaturated design investigates k factors in only n (<k+1) experimental runs. The goal for such a design is to identify, presumably only a few, relatively dominant effects with a cost as low as possible. While the construction of supersaturated designs has been widely explored, the data analysis aspect of such designs remains primitive. We study the following problem: How many dominant effects are allowed to make a meaningful data analysis possible for a supersaturated design with the maximum correlation ρ? The correlation here is defined as the cosine of the angle between two column vectors. The obtained results support the fundamental concern of the E(s2) criterion introduced by . Furthermore, under the normality assumption, we obtained a lower bound of the probability that the factor with the largest estimated effect has, indeed, the largest true effect. This bound depends on the relative size of the largest effect and the maximum correlation of the underlying design. Under some mild assumptions, we show that this probability is satisfactorily large. Consequently, by carefully constructing supersaturated designs, we not only save the cost of the experiment, but also make reliable inferences.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics