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On aliasing and generalized defining relationships of factorial arrangements
Author(s) -
Raktoe B. L.,
Pesotan H.,
Federer W. T.
Publication year - 1980
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3314671
Subject(s) - factorial , mathematics , fractional factorial design , orthogonality , aliasing , factorial experiment , uniqueness , fraction (chemistry) , prime (order theory) , terminology , arithmetic , algebra over a field , pure mathematics , discrete mathematics , filter (signal processing) , combinatorics , statistics , computer science , mathematical analysis , geometry , linguistics , philosophy , chemistry , organic chemistry , computer vision
The concepts of defining contrast (DC), generalized defining relationship (GDR) and aliasing structure (AS) are now well established in the terminology of regression analysis and factorial design theory. There is no complete agreement in the literature about the meaning of regular and irregular fractional factorial designs. This paper provides a workable definition of a regular fraction from a symmetrial prime‐powered factorial. It characterizes the uniqueness of the GDR for fractions from the most general factorial. Results are also présentés on the uniqueness of the GDR for regular designs, on orthogonality aspects of regular and irregular designs, and on group‐theoretic generation of the complete aliasing structure. Examples are provided to illustrate the developments.