Welcome to Objective Design of Experiments - Teaching practical, efficient experiment design to scientists, chemists and engineers

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A Brief Gosset Tutorial

The first step in generating a design with Gosset is to write a program describing the experimental situation. Let's assume we want to generate an I-Optimal design for 8 factors with a full quadratic model. We also want to have three trials more than the minimum required. The Gosset program for this is,

10 range X1 X2 X3 X4 X5 X6 X7 X8 -1 1
20 model (1+X1+X2+X3+X4+X5+X6+X7+X8)^2

This simple program specifies the situation. Notice that each line requires a line number. The commands will be executed in numerical order. The command "range" specifies the low and high levels for continuous factors. In this case, all of the factors from X1 to X8 will range from -1 to 1.

The "model" command requires a little more explanation. Notice that if you multiply (1+X1+X2+X3+X4+X5+X6+X7+X8) *(1+X1+X2+X3+X4+X5+X6+X7+X8) you get 1+X1+X2+...+X8_X1X2+X1X3+...+X7X8+X1^2+X2^2+...+X8^2 - the full quadratic model with all 2-factor interactions, but with the b coefficients missing. Gosset knows you want the b coefficients. This is a shorthand for model specification. If you wish to subtract terms from the model, simply subtract them at the end of line 20 above.

Now that we have the program, we need to compile it. This is accomplished by simply typing "c" and pressing return. Gosset will provide a list of terms in your model. If the list looks like you expected, you are doing things right.

The next step is to compute the "moments matrix." This is a mathematical detail handled by Gosset. All we need to do is type

"m n=100000"

and press return. When Gosset is done, it will let us know.

Last, we have to generate the actual design. To do this, we type

"d n=100 extra=3 tiny=1e-5 type=I"

and press return. "n=100" tells Gosset to generate 100 designs and keep the best. "extra=3" tells Gosset to include 3 more trials in the design than the minimum required. "tiny=1e-5" tells Gosset the smallest difference to consider to be real. "type=I" tells Gosset to generate an I-Optimal design.

We will see a list of the progress as Gosset works. When it is finished, we type "interp" to see the design.