Design and Analysis of Experiments by Douglas Montgomery. Heath Rushing
table. For the remainder of the text, we will assume that the data tables are created in JMP.
Section 3.1 A One-way ANOVA Example
1. Open Etch-Rate-Import.jmp.
2. Click the blue icon (triangle) next to Power in the Columns panel and select Nominal.
Even though the levels of Power are ordinal, we are not incorporating that information into the current analysis. This distinction is not critical since Power is only a factor, and not the response. Treating an ordinal factor as nominal yields the same model fit. For a response variable, a nomial modeling type prompts a multinomial logistic regression, while an ordinal modeling type prompts an ordered logistic regression.
3. Select Analyze > Fit Y by X.
4. Select Etch Rate and click Y, Response.
5. Select Power and click X, Factor.
6. Click OK.
7. To produce a box plot, click the red triangle next to One-way Analysis of Etch Rate By Power and select Quantiles.
The box plots show that the etch rate increases as power increases, and that the variability of the etch rate is roughly the same for each power setting.
8. Select Window > Close All. We will now demonstrate how this model can be created in JMP.
9. Select DOE > Full Factorial Design.
10. Under Response Name, double click Y and change the response name to Etch Rate.
11. In the Factors section, select Categorical > 4 Level.
12. Double-click the name of the new factor, X1, and change it to Power.
13. Likewise, change the Values of the new factor from L1, L2, L3, and L4 to 160, 180, 200, and 220, respectively.
14. Click Continue.
15. Leave Run Order set to Randomize. Then, the experiment should be run in the order in which the rows appear in the resulting JMP table.
Number of Runs: 4 indicates that the design requires four different runs. Once Make Table has been clicked, Number of Runs will change to 20, reflecting the runs needed for the four replicates.
16. Enter 4 for Number of Replicates. This indicates the original 4 runs will be replicated 4 times for a total of 20 runs.
17. Click Make Table.
A new data table has been created with three columns. The Pattern column indicates which combination of factor levels are being used for the current row. Since there is only one factor, Power, the Pattern column simply indicates which level of Power is being run. The Power column has automatically been set to the Nominal modeling type. Additional metadata about the columns has been included from the Full Factorial platform, as indicated by the
All of the JMP platforms demonstrated in this book are capable of fitting models in the presence of missing data. That is, if it is not possible to perform the 20th run, which is at the Power setting of 220, it would still be possible to analyze the first 19 runs. However, missing observations can affect the aliasing structure of a design, which will be discussed in later chapters. In addition, if the cause of the missing values is related to the response (missing not at random), then the resulting estimates could be biased.
18. 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