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Introduction to the FACTEX Procedure 
See FACTEX3 in the SAS/QC Sample Library 
Often you do not have the resources for a full factorial design. In this case, a fractional factorial design is a reasonable alternative, provided that the effects of interest can be estimated.
Box, Hunter, and Hunter (1978) describe a fractional factorial design for studying a chemical reaction to determine what percentage of the chemicals responded in a reactor. The researchers identified the following five treatment factors that were thought to influence the percentage of reactant:
The complete 2^{5} factorial design requires 32 runs, but it was decided to use a halffraction design, which requires 16 runs.
Suppose that all main effects and twofactor interactions are to be estimated. An appropriate design for this situation is a design of resolution 5 (denoted as 2^{51}_{V}), in which no main effect or twofactor interaction is aliased with any other main effect or twofactor interaction but in which twofactor interactions are aliased with threefactor interactions. This design loses the ability to estimate interactions between three or more factors, but this is usually not a serious loss. For more on resolution, see "Resolution" .
You can use the following statements to construct a 16run factorial design that has five factors and resolution 5:
proc factex; factors feedrate catalyst agitrate temperat concentn; size design=16; model resolution=5; output out=reaction feedrate nvals=(10 15 ) catalyst nvals=(1 2 ) agitrate nvals=(100 120) temperat nvals=(140 180) concentn nvals=(3 6 ); proc print; run;
The design saved in the REACTION data set is listed in Figure 14.5.
The use of a halffraction causes some interaction terms to be confounded with each other. You can use the EXAMINE statement with the ALIASING option to determine which interaction terms are aliased, as follows:
proc factex; factors feedrate catalyst agitrate temperat concentn; size design=16; model resolution=5; examine aliasing; run;
The alias structure summarizes the estimability of all main effects and two and threefactor interactions. Figure 14.6 indicates that each of the threefactor interactions is confounded with a twofactor interaction. Thus, if a particular threefactor interaction is believed to be significant, the aliased twofactor interaction cannot be estimated with this halffraction design.

When you submit the preceding statements, the following message is displayed in the SAS log:
NOTE: Design has 16 runs, resolution = 5.
This message confirms that the design exists. If you specify a factorial design that does not exist, an error message is displayed in the SAS log. For instance, suppose that you replaced the MODEL statement in the preceding example with the following statement:
model resolution=6;
Since the maximum resolution of a 2^{51} design is 5, the following message appears in the SAS log:
ERROR: No such design exists.
In general, it is good practice to check the SAS log to see if a design exists.
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