Construct an Accurate Confidence Interval for Variance Components
Construct the Design
If you prefer to skip the steps in this section, select Help > Sample Data Library and open Design Experiment/Catalyst In the Catalyst data table, click the green triangle next to the DOE Simulate script. Then go to Fit the Model.
Select DOE > Custom Design.
Click Add Factor > Continuous.
Double-click to rename these factors Temperature, Time, and Catalyst.
For Temperature, click Easy and select Very Hard.
This defines Temperature to be a whole plot factor.
For Time, click Easy and select Hard for Time.
This defines Time to be a subplot factor.
Click Continue.
Note: Setting the Random Seed in step 10 and Number of Starts in step 11 reproduces the exact results shown in this example. In constructing a design on your own, these steps are not necessary.
(Optional) Click the Custom Design red triangle and select Set Random Seed. Type 12345 and click OK.
(Optional) Click the Custom Design red triangle and select Number of Starts. Type 1000 and click OK.
Click Make Design.
Click Make Table.
Note: The entries in your Y and Y Simulated columns will differ from those that appear in Design Table.
Design Table
Simulate Responses Window
The design table and a Simulate Responses window appear. Notice that the design table contains a DOE Simulate script. At any time, you can run this script to specify different parameter values.
Fit the Model
In the Distribution panel (Simulate Responses Window), next to Whole Plots σ, type 2.
Next to Subplots σ, type 1.5.
Click Apply.
In the data table, the formula for Y Simulated updates to reflect your specifications. To view the formula, click on the plus sign to the right of the column name in the Columns panel.
Click the Y variable next to the Y button and click Remove.
Click Y Simulated and click the Y button.
This action replaces Y with a column that contains a simulation formula.
Click Run.
Note: Because the values in Y Simulated are randomly generated, the entries in your report will differ from those that appear in REML Report Showing Wald Confidence Intervals.
REML Report Showing Wald Confidence Intervals
Explore Power
Simulate Window
In your simulations, you replace the column Y Simulated, which you used to run your model, with a new instance of the column Y Simulated, which generates a new column of simulated values for each simulation. The column on which you right-clicked and that appears as selected, Var Component, will be simulated for each effect listed in the Parameter Estimates table.
Next to Number of Samples, enter 200.
(Optional) Next to Random Seed, enter 456.
Table of Simulated Results for Var Component (Partial View)
Run the Distribution script.
Distribution Plots for Variance Components (Partial View)

Help created on 9/19/2017