The FACTEX Procedure |
[See FACTEX10 in the SAS/QC Sample Library]Folding over a fractional factorial design is a method for breaking the links between aliased effects in a design. Folding over a design means adding a new fraction identical to the original fraction except that the signs of all the factors are reversed. The new fraction is called a fold-over design. Combining a fold-over design with the original fraction converts a design of odd resolution into a design of resolution . 1 For example, folding over a resolution 3 design yields a resolution 4 design. You can use the FACTEX procedure to construct the original design fraction and a DATA step to generate the fold-over design.
Consider a fraction of a factorial design with factors A, B, C, D, E, and F. The following statements construct a design:
proc factex; factors A B C D E F; size fraction=8; model resolution=3; examine aliasing; output out=Original; run;
title 'Original Design'; proc print data=Original; run;
The option FRACTION=8 of the SIZE statement specifies a fraction of a complete factorial—that is, 8 (=). The design, which is saved in the data set Original, is displayed in Output 7.4.1.
Since the design is of resolution 3, the alias structure in Output 7.4.2 indicates that all the main effects are confounded with the two-factor interactions.
Aliasing Structure |
---|
A = C*F = D*E |
B = C*E = D*F |
C = A*F = B*E |
D = A*E = B*F |
E = A*D = B*C |
F = A*C = B*D |
A*B = C*D = E*F |
To separate the main effects and the two-factor interactions, augment the original design with a 1/8 fraction in which the signs of all the factors are reversed. The combined design (original design and fold-over design) of resolution 4 breaks the alias links between the main effects and the two-factor interactions. The fold-over design can be created by using the following DATA step:
data FoldOver; set Original; A=-A; B=-B; C=-C; D=-D; E=-E; F=-F; run; title 'Fold-Over Design'; proc print data=FoldOver; run;
Here, the data step creates the fold-over fraction by reversing the signs of the values of the factors in the original fraction. The fold-over design is displayed in Output 7.4.3.
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