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 Macros for the Design and Analysis of Experiments

# Fractional Factorial Design Macros: ADXFF File

The ADXFF file contains five macros and the ADXFFD SAS data set. These macros are used to construct and manipulate orthogonal fractional factorial designs for two-level factors. Two kinds of orthogonal designs are available: orthogonally confounded designs and Plackett-Burman screening designs.

In orthogonally confounded designs, any two effects (main effects or interactions) are either orthogonal or totally confounded. Effects that are totally confounded cannot be estimated separately. As designs decrease in size, fewer and fewer effects are estimable. One goal of design is to keep the effects of interest unconfounded with each other.

The resolution of a design indicates what kinds of effects are confounded with each other. In resolution 5 designs, main effects and two-factor interactions are all estimable and unconfounded with each other. In resolution 4 designs, two-factor interactions are confounded with each other, but they are free of main effects. In resolution 3 designs, main effects are confounded with two-factor interactions. Choose a design with maximum resolution, subject to your particular constraints on the number of runs you can make. See the "Resolution" section in Part 3, "The FACTEX Procedure," for more details about design resolution.

The macros in the ADXFF file enable you to construct orthogonal fractional factorial designs for as many as 11 treatments, as many as 128 runs, optionally in blocks with as few as 2 runs. If you require more specialized fractional factorial designs, you should use the FACTEX procedure; see Part 3, "The FACTEX Procedure."

You can also use the macros to construct Plackett-Burman designs for up to 47 two-level factors. Plackett-Burman designs are used to estimate the main effects of a large number of factors in as few runs as possible. They are sometimes known as screening designs because they are used at the initial stages of experimentation to identify important factors. However, there is no protection against two-factor interactions, so these designs should be used with caution.

The macros contained in ADXFF are as follows:

 ADXALIAS computes the alias structure of fractional factorial designs. ADXFFA analyzes fractional factorial designs. ADXFFD constructs fractional factorial designs. ADXPBD constructs Plackett-Burman designs. ADXPFF lists available fractional factorial designs.

Additionally, the ADXFFD data set is created in your work library. This data set contains the parameters for all possible orthogonally confounded designs of 128 or fewer runs.

The next six sections describe the macros and data set introduced above.