On Alias Matrices and Generalized Defining Relationships of Equi-Information Factorial Arrangements Free

In many practical situations a fraction of the full replicate of a k  ₁ x k  ₂ x ... x k_t factorial is used by an experimenter to estimate a subset of effects under the assumption that the rest of the effects are negligible. to get a deeper insight in what precisely is being estimated if the assumption of negligibility of the suppressed effects is not valid it is imperative that the experimenter has a complete knowledge of the aliasing structure. This paper shows how to compute the aliasing structure and hence the generalized defining relationship of any design in a particular class of equi-information designs, the class being generated by the action of the group of level permutations on a given design. It is shown that the calculations in the case of the 2' factorial are extremely simple and a practical example is given to illustrate the results.