In the early stages of studying a process, you identify a list of factors that potentially affect your response or responses. You are interested in identifying the active factors, that is, the factors that actually do affect your response or responses. A screening design helps you determine which factors are likely to be active. Once the active factors are identified, you can construct more sophisticated designs, such as response surface designs, to model interactions and curvature.
 • Design That Estimates Main Effects Only
 • Design That Estimates All Two-Factor Interactions
 • Design That Avoids Aliasing of Main Effects and Two-Factor Interactions
 • Supersaturated Screening Designs
 • Design for Fixed Blocks
 1 Select DOE > Custom Design.
 2 In the Factors outline, type 6 next to Add N Factors.
 3 Click Add Factor > Continuous.
 4 Click Continue.
Custom Design Window Showing Model Outline
Note: Setting the Random Seed in step 5 and Number of Starts in step 6 reproduces the exact results shown in this example. When constructing a design on your own, these steps are not necessary.
 5 (Optional) From the Custom Design red triangle menu, select Set Random Seed, type 1839634787, and click OK.
 6 (Optional) From the Custom Design red triangle menu, select Number of Starts, type 1, and click OK.
 7 Click Make Design.
Design for Main Effects Only
 8 Open the Design Evaluation > Color Map on Correlations outline.
Color Map on Correlations
 ‒ The main effects are represented by the six terms in the upper left corner of the map.
 ‒ Notice that no effects are completely confounded with each other. The only red squares, indicating absolute correlations of 1, are on the main diagonal.
 9 Open the Design Evaluation > Alias Matrix outline.
Alias Matrix
The Alias Matrix shows how the coefficients of the main effect terms in the model are biased by potentially active two-factor interaction effects. The column labels identify interactions. For example, in the X1 row, the column X2*X3 has a value of 0.333 and the column X2*X4 has a value of -0.33. This means that the expected value of the main effect of X1 is the sum of the main effect of X1 plus 0.333 times the effect of X2*X3, plus -0.33 times the effect of X2*X4, and so on, for the rest of the X1 row. In order for the estimate of the main effect of X1 to be meaningful, you must assume that these interactions are negligible in size compared to the effect of X1.
The Alias Matrix in Alias Matrix shows partial aliasing of effects. In other cases, main effects might be fully aliased, or confounded, with two-factor interactions. In both of these cases, strong two-factor interactions can confuse the results of main effects only experiments. To avoid this risk, create a design that resolves all two-factor interactions.
 1 Select DOE > Custom Design.
 2 Type 5 next to Add N Factors.
 3 Click Add Factor > Continuous.
 4 Click Continue.
 5 In the Model outline, select Interactions > 2nd.
Model Outline Showing Interactions
 6 Click Minimum to accept 16 for the number of runs.
Note: Setting the Random Seed in step 7 and Number of Starts in step 8 reproduces the exact results shown in this example. In constructing a design on your own, these steps are not necessary.
 7 (Optional) From the Custom Design red triangle menu, select Set Random Seed, type 819994207, and click OK.
 8 (Optional) From the Custom Design red triangle menu, select Number of Starts, type 1, and click OK.
 9 Click Make Design.
Design to Estimate All Two-Factor Interactions shows the runs of the design. All main effects and two-factor interactions are estimable because their Estimability was designated as Necessary (by default) in the Model outline.
Design to Estimate All Two-Factor Interactions
 10 Open the Design Evaluation > Color Map on Correlations outline.
Color Map on Correlations
In this example, you find a compromise between an 8-run main effects only design (see Design That Estimates Main Effects Only) and a 22-run design capable of fitting all the two-factor interactions. You use Alias Optimality as the optimality criterion to achieve your goal.
 1 Select DOE > Custom Design.
 2 Type 6 next to Add N Factors.
 3 Click Add Factor > Continuous.
 4 Click Continue.
 5 Select Optimality Criterion > Make Alias Optimal Design from the red triangle menu.
 6 Click User Specified and change the number of runs to 16.
Factors, Model, Alias Terms, and Number of Runs
Note: Setting the Random Seed in step 7 and Number of Starts in step 8 reproduces the exact results shown in this example. In constructing a design on your own, these steps are not necessary.
 7 (Optional) From the Custom Design red triangle menu, select Set Random Seed, type 1692819077, and click OK.
 8 (Optional) From the Custom Design red triangle menu, select Number of Starts, type 161, and click OK.
 9 Click Make Design.
 10 Open the Design Evaluation > Alias Matrix outline.
Alias Matrix
 11 Open the Design Evaluation > Color Map on Correlations outline.
Color Map on Correlations
In a saturated design, the number of runs equals the number of model terms. In a supersaturated design, the number of model terms exceeds the number of runs (Lin, 1993). A supersaturated design can examine dozens of factors using fewer than half as many runs as factors. This makes it an attractive choice for factor screening when there are many factors and experimental runs are expensive.
 • If the number of active factors is more than half the number of runs in the experiment, then it is likely that these factors will be impossible to identify. A general rule is that the number of runs should be at least four times larger than the number of active factors. In other words, if you expect that there might be as many as five active factors, you should plan on at least 20 runs.
 • Analysis of supersaturated designs cannot yet be reduced to an automatic procedure. However, using forward stepwise regression is reasonable. In addition, the Screening platform (Analyze > Modeling > Screening) offers a streamlined analysis.
 1 Select DOE > Custom Design.
 2 Type 12 next to Add N Factors.
 3 Click Add Factor > Continuous.
 4 Click Continue.
 5 In the Model outline, select all terms except the Intercept.
 6 Click Necessary next to any effect and change it to If Possible.
Factors, Model, and Number of Runs
 7
 8 Select Simulate Responses from the red triangle menu.
Note: Setting the Random Seed in step 9 and Number of Starts in step 10 reproduces the exact results shown in this example. In constructing a design on your own, these steps are not necessary.
 9 (Optional) From the Custom Design red triangle menu, select Set Random Seed, type 1008705125, and click OK.
 10 (Optional) From the Custom Design red triangle menu, select Number of Starts, type 100, and click OK.
 11 Click Make Design.
 12 Click Make Table.
Design Table with Simulated Responses
The response column, Y, contains simulated values. These are randomly generated using the model defined by the parameter values in the Simulate Responses window.
Simulate Responses Window
The Simulate Responses window shows coefficients of 0 for all terms, with an Error Std of 1. The values in the Y column currently reflect only random variation. Notice that the model coefficients are set to 0 because not all coefficients are estimable.
 13
Parameter Values for Simulated Responses
 14 Click Apply.
Response Column with X1 and X11 Active
In your simulation, you specified X1 and X11 as active factors with large effects relative to the error variation. For this reason, your analysis of the data should identify these two factors as active.
The Screening platform provides a way to identify active factors. The design table in Response Column with X1 and X11 Active contains three scripts. The Screening script analyzes your data using the Screening platform (located under the Analyze > Modeling > Screening menu).
 1 In the Tables panel of the design table, select Run Script from the red triangle next to Screening.
Screening Report for Supersaturated Design
The factors X1 and X11 have large contrast and Lenth t-Ratio values. Also, their Simultaneous p-Values are small. In the Half Normal Plot, both X1 and X11 fall far from the line. The Contrasts and the Half Normal Plot reports indicate that X1 and X11 are active. Although X12 has an Individual p-Value less than 0.05, its effect is much smaller than that of X1 and X11.
Because the design is supersaturated, p-values might be smaller than they would be in a model where all effects are estimable. This is because effect estimates are biased by other potentially active main effects. In Screening Report for Supersaturated Design, a note directly above the Make Model button warns you of this possibility.
 2 Click Make Model.
 3 Click Run in the Model Specification window.
Parameter Estimates for Model
Note that the parameter estimates for X11 and X1 are close to the theoretical values that you used to simulate the model. See Parameter Values for Simulated Responses, where you specified a model with X1 = 10 and X11 = 10. The significance of the factor X12 is an example of a false positive.
 4 In your Custom Design window, open the Design Evaluation > Color Map on Correlations outline.
Color Map on Correlations Outline
With your cursor, place your mouse pointer over cells to see the absolute correlations. Notice that X1 has correlations as high as 0.5 with other main effects (X4, X5, X7).
Stepwise regression is another way to identify active factors. The design table in Response Column with X1 and X11 Active contains three scripts. The Model script analyzes your data using stepwise regression in the Fit Model platform.
 1 In the Tables panel of the design table, select Run Script from the red triangle next to Model.
 2 Change the Personality from Standard Least Squares to Stepwise.
 3 Click Run.
 4 In the Stepwise Fit for Y report, change the Stopping Rule to Minimum AICc.
 5 Click Go.
Stepwise Regression for Supersaturated Design
Stepwise Regression for Supersaturated Design shows that the selected model consists of the two active factors, X1 and X11. The step history appears in the bottom part of the report. Keep in mind that correlations between X1 and X11 and other factors could mask the effects of other active factors. See Color Map on Correlations Outline.
 1 Select DOE > Custom Design.
 2 In the Factors outline, type 3 next to Add N Factors.
 3 Click Add Factor > Continuous.
 4 Click Add Factor > Blocking > 3 runs per block.
Note that the blocking factor X4 shows only one level under Values. This is because the run size is unknown at this point. Once you click Continue, the Factors outline shows an appropriate number of blocks, calculated as the Default run size divided by the number of runs per block. If you specify a different run size, the Factors outline updates to show the appropriate number of values for the blocking factor.
Factors Outline Showing One Block for X4
 5 Click Continue.
Factors Outline Showing Three Blocks for X4
 6 Select the three continuous factors, X1, X2, and X3, in the Factors outline.
 7 In the Model outline, click Interactions > 2nd.
Factors Outline Showing Six Blocks for X4
Note: Setting the Random Seed in step 8 and Number of Starts in step 9 reproduces the exact results shown in this example. In constructing a design on your own, these steps are not necessary.
 8 (Optional) From the Custom Design red triangle menu, select Set Random Seed, type 458027747, and click OK.
 9 (Optional) From the Custom Design red triangle menu, select Number of Starts, type 10, and click OK.
 10 Click Make Design.
Fixed Block Design
The Design outline shows the design. Recall that X4 is the blocking factor. Observe that the six blocks are represented. When you conduct your experiment, you run the three trials where X4 = 1 on the first day, the three where X4 = 2 on the second day, and so on. So you would like the design table to randomize the trials within blocks. In the Output Options panel, note that Randomize within Blocks is the default setting for Run Order.
 11 Click Make Table.
Design Table for Fixed Block Design