Detection of interactions in experiments on large numbers of factors

One of the main advantages of factorial experiments is the information that they can offer on interactions. When there are many factors to be studied, some or all of this information is often sacrificed to keep the size of an experiment economically feasible. Two strategies for group screening are p resented for a large number of factors, over two stages of experimentation, with particular emphasis on the detection of interactions. One approach es timates only main effects at the first stage (classical group screening), w hereas the other new method (interaction group screening) estimates both ma in effects and key two-factor interactions at the first stage. Three criter ia are used to guide the choice of screening technique, and also the size o f the groups of factors for study in the first-stage experiment. The criter ia seek to minimize the expected total number of observations In the experi ment, the probability that the size of the experiment exceeds a prespecifie d target and the proportion of active individual factorial effects which ar e not detected. To Implement these criteria, results are derived on the rel ationship between the grouped and individual factorial effects, and the pro bability distributions of the numbers of grouped factors whose main effects or interactions are declared active at the first stage. Examples are used to illustrate the methodology, and some issues and open questions for the p ractical implementation of the results are discussed.