Analyzing a Supersaturated Design

Supersaturated designs have more factors than runs. The objective is to determine which effects are active. They rely heavily on effect sparsity for their analysis, so the Fit Two Level Screening platform is ideal for their analysis.

As an example, look at Supersaturated.jmp, from the sample data folder, a simulated data set with 18 factors but only 12 runs. Y is generated by

where ε ~ N(0,1). So, Y has been constructed with three active factors.

To detect the active factors, run the Fit Two Level Screening platform with X1–X18 as X and Y as Y. The report shown in Screening Report for Supersaturated.jmp appears.

Screening Report for Supersaturated.jmp

Note that the three active factors have been highlighted. One other factor, X18, has also been highlighted. It shows in the Half Normal plot close to the blue line, indicating that it is close to the 0.1 cutoff significance value. The 0.1 critical value is generous in its selection of factors so you don’t miss those that are possibly active.

The contrasts of 5.1, –3, and 1.8 are close to their simulated values (5, –3, 2). However, the similarity of these values can be increased by using a regression model, without the effect of orthogonalization.

The p-values, while useful, are not entirely valid statistically, since they are based on a simulation that assumes orthogonal designs, which is not the case for supersaturated designs.