Modeling and Multivariate Methods - SAS

Chapter 8 Analyzing Screening Designs 239
Statistical Details
• If no effect in the model is active after the intercept, the contrasts are just an orthogonal rotation of
random independent variates into different random independent variates. These newly orthogonally
rotated variates have the same variance as the original random independent variates. To the extent that
some effects are active, the inactive effects still represent the same variation as the error in the model.
The hope is that the effects and the design are strong enough to separate the active effects from the
random error effects.
Lenth’s Pseudo-Standard Error
At this point, Lenth’s method (Lenth, 1989) identifies inactive effects from which it constructs an estimate
of the residual standard error, known as the Lenth Pseudo Standard Error (PSE).
The value for Lenth’s PSE is shown at the bottom of the Screening report. From the PSE, t-ratios are
obtained. To generate p-values, a Monte Carlo simulation of 10,000 runs of n – 1 purely random values is
created and Lenth t-ratios are produced from each set. The p-value is the interpolated fractional position
among these values in descending order. The simultaneous p-value is the interpolation along the max(|t|) of
the n – 1 values across the runs. This technique is similar to that in Ye and Hamada (2000).
If you want to run more or less than the 10,000 default runs, you must assign a value to a global JSL variable
named LenthSimN. As an example, using the sample data Reactor Half Fraction.jmp:
1. Open the sample data, Reactor Half Fraction.jmp.
2. Select Analyze > Modeling > Screening.
3. Select Percent Reacted as the response variable, Y.
4. Select all the other continuous variables as effects, X.
5. Click OK.
6. Select Script > Save Script to Script Window from the red-triangle menu of the report.
7. Add LenthSimN=50000; to the top of the Script Window (above the code).
8. Highlight LenthSimN=50000; and the remaining code.
9. Run the script from the Script Window.
Note that if LenthSimN=0, the standard t-distribution is used (not recommended).