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3.
Simulate likelihood ratio test p-values to explore the power of detecting a difference over a range of probability values that is determined by the linear predictor. See Explore Power.
where π(X) denotes the probability that a part passes at the given design settings X = (X1X2, ..., X6).
X1
X2
X3
X4
X5
X6
For example, when all factors other than X1 are set to 0, the difference in pass rates that you want to detect is 46.2%. The smallest difference in pass rates that you want to detect occurs when all factors other than X6 are set to zero and that difference is 24.5%.
Note: If you prefer to skip the steps in this section, select Help > Sample Data Library and open Design Experiment/Binomial Experiment.jmp. Click the green triangle next to the DOE Simulate script and then go to Define Simulated Responses.
1.
Select DOE > Custom Design.
3.
Click Add Factor > Continuous.
4.
Click Continue.
Note: Setting the Random Seed in step 7 and Number of Starts in step 8 reproduces the same design shown in this example. In constructing a design on your own, these steps are not necessary.
7.
(Optional) Click the Custom Design red triangle and select Set Random Seed. Type 12345 and click OK.
8.
9.
Click Make Design.
10.
Click Make Table.
Note: The entries in your Y and Y Simulated columns will differ from those that appear in Figure 10.17.
Figure 10.17 Partial View of Design Table
Figure 10.18 Simulate Responses Window
Y contains a set of values simulated according to the specifications in the Simulate Responses window.
Y Simulated contains a formula that calculates its values using the formula for the model that is specified in the Simulate Responses window. To view the formula, click on the plus sign to the right of the column name in the Columns panel.
1.
In the Simulate Responses window (Figure 10.18), type the following values under Y:
Next to X1, 1 is entered by default. Keep that value.
Next to X2, type 0.9.
Next to X3, type 0.8.
Next to X4, type 0.7.
Next to X5, type 0.6.
Next to X6, type 0.5.
Leave the value for N set to 1, indicating that there is only one unit per trial.
Figure 10.19 Completed Simulate Responses Window
3.
Click Apply.
In the design data table, the Y Simulated column is replaced with a formula column that generates binomial values. A column called Y N Trials indicates the number of trials for each run.
4.
(Optional) Click on the plus sign to the right of Y Simulated in the Columns panel.
Figure 10.20 Random Binomial Formula for Y Simulated
5.
Click Cancel.
2.
Click the Y variable next to the Y button and click Remove.
3.
Click Y Simulated and click the Y button.
You are replacing Y with a column that contains randomly generated binomial values.
4.
From the Personality menu, select Generalized Linear Model.
6.
Click Run.
1.
In the Effect Tests outline, right-click in the Prob>ChiSq column and select Simulate.
Figure 10.21 Simulate Window
Make sure the Y Simulated column is selected in the Column to Switch Out list. This column contains the values that were used to fit the model. When you select the column Y Simulated under Column to Switch In, for each simulation, you are telling JMP to replace the values in Y Simulated with a new column of values that are simulated using the formula in the column Y Simulated.
The column you have selected in the report, Prob>ChiSq, is the p-value for a likelihood ratio test of whether the associated main effect is 0. The Prob>ChiSq value will be simulated for each effect listed in the Effect Tests table.
2.
Next to Number of Samples, enter 500.
3.
Note: Because response values are simulated, your simulated p-values will differ from those shown in Figure 10.22.
Figure 10.22 Table of Simulated Results, Partial View
The first row of the table contains the initial values of Prob>ChiSq and is excluded. The remaining 500 rows contain simulated values.
4.
Run the Power Analysis script.
Figure 10.23 Distribution Plots for the First Three Effects
6.
Press Ctrl and click the X1 red triangle, and de-select Outlier Box Plot.
7.
Press Ctrl and click the X1 red triangle, then select Histogram Options and de-select Histogram.
Figure 10.24 Power Results for the First Three Effects
In the Simulated Power outlines, the Rejection Rate for each row gives the proportion of p-values that are smaller than the corresponding Alpha. For example, for X3, which corresponds to a coefficient value of 0.8 and a probability difference of 38%, the simulated power for a 0.05 significance level is 379/500 = 0.758. Table 10.1 summarizes the estimated power at the 0.05 significance level for all effects. Notice how power decreases as the Difference to Detect decreases. Also notice that the power to detect an effect as large as 24.5% (X6) is only approximately 0.37.
X1
X2
X3
X4
X5
X6

Help created on 3/19/2020