On a heuristic analysis of highly fractionated 2 n factorial experiments

The paper deals with a method for the analysis of highly fractionated factorial designs proposed by Raghavarao and Altan in Metrika 58:185–191 (2003). We show that the method will find “active” factors with almost any set of random numbers. Once that an alias set is found active, Raghavarao and Altan claim that their method can resolve the alias structure of the design and identify which of several confounded effects is active. We show that their method cannot do that. The error in Raghavarao and Altan’s arguments lies in the fact that they treat a set of highly dependent (sometimes even identical) F-statistics as if they were independent.