Example of evaluating a design
main topic     interpreting results     session command     see also     

Suppose you want determine how reducing the model changes the optimality for the 20 point experimental design obtained in the Example of selecting a D-optimal response surface design. Remember that a model that is D-optimal for a given model only.

1    Open the worksheet OPTDES3.MTW. (The design and indicator columns have been saved for you.)

2    Choose Stat > DOE > Response Surface > Select Optimal Design.

3    Choose Evaluate design, then enter OptPoint in the box.

4    Click Terms.

5    From Include the following terms, choose Linear.

6    Click OK in each dialog box.

Session window output

Optimal Design: Blocks, A, B, C, D

 

 

Evaluation of Specified Response Surface Design

 

Number of design points in optimal design: 20

 

Model terms: Block, A, B, C, D

 

 

 

Specified Design

 

Row number of selected design points: 1, 3, 4, 6, 8, 9, 10, 13, 15, 16, 17, 19, 22, 23, 24,

                                      25, 26, 27, 28, 30

 

Condition number:                           1.43109

D-optimality (determinant of XTX):         47267840

A-optimality (trace of inv(XTX)):          0.320581

G-optimality (avg leverage/max leverage):  0.871492

V-optimality (average leverage):                0.3

Maximum leverage:                          0.344237

Interpreting the results

The Session window output contains the following four parts:

·    The number of points in the design.

·    The model terms. D-optimal designs depend on the specified model. In this example, the terms include:

Block A B C D

These are the linear model terms that you chose in the Terms subdialog box. Remember, a design that is D-optimal for one model will most likely not be D-optimal for another model.

·    The selected design points. The numbers shown identify the row of the design points in the worksheet.

·    In addition to the design's D-optimality, Minitab displays various optimality measures. You can use this information to evaluate or compare designs. If you compare the optimality of the 20-point design for a full quadratic model from the example of selecting a D-optimal response surface design with this 20-point design for a linear model, you will notice that the D-optimality decreased from 2.73819E+18 to 47267840. Larger D-optimality values indicate a more optimal design.