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

B. L. Raktoe
Journal of the Royal Statistical Society. Series B (Methodological)
Vol. 38, No. 3 (1976), pp. 279-283
Published by: Wiley for the Royal Statistical Society
Stable URL: http://www.jstor.org/stable/2984978
Page Count: 5
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On Alias Matrices and Generalized Defining Relationships of Equi- Information Factorial Arrangements
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Abstract

In many practical situations a fraction of the full replicate of a k1× k2×...× kt 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 2t factorial are extremely simple and a practical example is given to illustrate the results.

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