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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).
 Coefficient Value β0 0 β1 1 β2 .9 β3 .8 β4 .7 β5 .6 β6 .5
 Factor Percent Passing at Xi = 1 Percent Passing at Xi = -1 Difference X1 73.11% 26.89% 46.2% X2 71.09% 28.91% 42.2% X3 69.00% 31.00% 38.0% X4 66.82% 33.18% 33.6% X5 64.56% 35.43% 29.1% X6 62.25% 37.75% 24.5%
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.
 2 In the Factors outline, type 6 next to Add N Factors.
 3 Click Add Factor > Continuous.
 4 Click Continue.
 5 Under Number of Runs, type 60 next to User Specified.
 6 Click the Custom Design red triangle and select Simulate Responses.
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) Click the Custom Design red triangle and select Set Random Seed. Type 12345 and click OK.
 8 (Optional) Click the Custom Design red triangle and select Number of Starts. Type 1 and click OK.
 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 Partial View of Design Table.
Partial View of Design Table
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 (Simulate Responses Window), type the following values under Y:
 – Next to Intercept, type 0.
 – 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.
 2 In the Distribution outline, select Binomial.
Leave the value for N set to 1, indicating that there is only one unit per trial.
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.
Random Binomial Formula for Y Simulated
 5 Click Cancel.
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 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.
 5 From the Distribution menu, select Binomial.
 6 Click Run.
 1 In the Effect Tests outline, right-click in the Prob>ChiSq column and select Simulate.
Simulate Window
The column Y Simulated under the Column to Switch Out 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 (Optional) Next to Random Seed, enter 123 and then click outside the text box.
 4 Click OK.
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.
 5 Run the Power Analysis script.
Distribution Plots for the First Three Effects
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 7 Press Ctrl and click the X1 red triangle, and de-select Outlier Box Plot.
 8 Press Ctrl and click the X1 red triangle, then select Histogram Options and de-select Histogram.
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 that 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. Simulated Power at Significance Level 0.05 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.
 Factor Percent Passing at Xi = 1 Percent Passing at Xi = -1 Difference to Detect Simulated Power (Rejection Rate) at Alpha=0.05 X1 73.11% 26.89% 46.2% 0.852 X2 71.09% 28.91% 42.2% 0.828 X3 69.00% 31.00% 38.0% 0.758 X4 66.82% 33.18% 33.6% 0.654 X5 64.56% 35.43% 29.1% 0.488 X6 62.25% 37.75% 24.5% 0.372

Help created on 9/19/2017