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 Details of the FACTEX Procedure

## Example 15.3: Factorial Design with Center Points

 See FACTEX9 in the SAS/QC Sample Library

Factorial designs involving two levels are the most popular experimental designs. For two-level designs, it is assumed that the response is close to linear over the range of the factor levels. To check for curvature and to obtain an independent estimate of error, you can replicate points at the center of a two-level design. Adding center points to the design does not affect the estimates of factorial effects.

To construct a design with center points, you first create a data set with factorial points using the FACTEX procedure and then augment it with center points by using a simple DATA step. The following example illustrates this technique.

A researcher is studying the effect of three two-level factors -current (CURRENT), voltage (VOLTAGE), and time (TIME) -by conducting an experiment using a complete factorial design. The researcher is interested in studying the overall curvature over the range of factor levels by adding four center points.

You can construct this design in two stages. First, create the basic 23 design with the following statements:

```   proc factex;
factors current voltage time;
output out=factdat
current nvals=(12  28 )
voltage nvals=(100 200)
time    nvals=(50  60 );
run;
```

Next, create the center points and append to the basic design as follows:

```   data center(drop=i);
do i = 1 to 4;
current = 20;
voltage = 150;
time    = 55;
output;
end;
data cpdesgn;
set factdat center;
run;

proc print data=cpdesgn;
run;
```

The design saved in the data set CPDESIGN is displayed in Output 15.3.1. Observations 1 to 8 are the factorial points, and observations 9 to 12 are the center points.

Output 15.3.1: A 23 Design with Four Center Points

 Obs current voltage time 1 12 100 50 2 12 100 60 3 12 200 50 4 12 200 60 5 28 100 50 6 28 100 60 7 28 200 50 8 28 200 60 9 20 150 55 10 20 150 55 11 20 150 55 12 20 150 55

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