Select Window > Close All.
19. Open Etch-Rate.jmp. This data table was created in JMP using the Full Factorial Design platform.
20. Select Analyze > Fit Model.
Etch Rate is automatically populated into the Y field, and the nominal Power factor is automatically added as a model effect. The corresponding fields in the Fit Y by X platform will not be automatically populated. However, the Fit Model platform is more general than the Fit Y by X platform and will be used much more frequently. Setting default column roles for the Fit Y by X and other platforms may be achieved via the Cols > Preselect Role menu. Please note that this can also be accomplished by selecting Run Script from the (red triangle associated with the) Model script contained in the Table Panel of the data table.
21. Select Window > Close All.
Example 3.1 The Plasma Etching Experiment
1. Open Etch-Rate.jmp.
2. Select Analyze > Fit Y by X.
3. Select Etch Rate and click Y, Response.
4. Select Power and click X, Factor.
5. Click OK.
6. Click the red triangle next to One-way Analysis of Etch Rate By Power and select Means/Anova.
The p-value for the F test of the null hypothesis of the equality of treatment means is <.0001. We conclude that the treatment means differ.
7. Leave the Etch-Rate data table open for the next exercise.
Example 3.3 Treatment Effects and Confidence Intervals.
1. Return to the Etch-Rate data table.
2. Click Analyze > Fit Model. As shown in the first example of this chapter, the modeling roles are pre-specified. Unless a different model needs to be fit than the one specified by the script attached to the data table, the screenshot of the Fit Model platform may be omitted.
3. Click Run. As noted previously, the Fit Model platform could also have been launched by clicking the red triangle next to the Model script in the Etch-Rate data table and clicking Run Script. This script was created by the Full Factorial Design platform and attached to the data table produced therein.
4. Scroll down to the Parameter Estimates report. It may be necessary to click the gray triangle next to the report title in order to expand the output window.
The coefficients for power settings of 160, 180, and 200 provided by JMP match those in the textbook. The intercept represents the grand mean of the observations.
5. To see the estimate for 220, click the red triangle next to Response Etch Rate and select Estimates > Expanded Estimates.
6. To display the confidence intervals for the parameter estimates, right-click inside the Expanded Estimates report, and select Columns > Lower 95% and Columns > Upper 95%.
Alternatively, you can click the red triangle next to Response Etch Rate and select Regression Reports > Show All Confidence Intervals.
7. In addition to viewing the Expanded Estimates, you can also click the red triangle next to Response Etch Rate and select Effect Screening > Scaled Estimates.
8. The Scaled Estimates report produces the same output as the Expanded Estimates report, in addition to a graphical representation of the magnitude of the treatment effects.
9. By clicking the red triangle next to Response Etch Rate and selecting Factor Profiling > Profiler, you obtain an interval plot of the mean responses and their confidence intervals.
The Prediction Profiler provides the estimate mean response together with a confidence interval for each power setting. We will not explore the full functionality of the Prediction Profiler here, but it may be used for optimizing parameter settings to achieve a desired response.
10. Leave the Fit Model platform open for the next exercise.
Section 3.4 Model Adequacy Checking
1. In the Fit Model platform from the previous exercise, scroll down to the Residuals by Predicted plot. This plot is discussed in Section 3.4.3 of the textbook.
The variance appears to be constant across the range of predicted etch rates, and no patterns emerge from the plot. Because only a single categorical factor, Power, is included in the model, the validity of the assumption of constant residual variance may also be checked with formal tests, as described in Example 3.4.
2. To check the normality assumption, a quantile plot is commonly used. In JMP, the first step is to generate residuals for each observation. Click the red triangle next to Response Etch Rate and select Save Columns > Residuals.
3. Return to the Etch-Rate data table (you can use a shortcut by clicking the table icon
4. Click Analyze > Distribution.
5. Select Residual Etch Rate for Y, Columns.
6. Click OK.
7. Click the red triangle next to Residual Etch Rate and select Continuous Fit > Normal.
8. Scroll down and click the red triangle next to Fitted Normal and select Diagnostic Plot.
The error distribution appears to be approximately normal as the points fall relatively close to a straight line. We may also perform a Shapiro-Wilk test for the hypothesis that the residuals are from a normal distribution.
9. Click the red triangle next to Fitted Normal and select Goodness of Fit.
With a p-value of 0.2152, the residuals do not display a significant number of departures from normality.
