When any DOE platform other than Accelerated Life Test Design creates a design, JMP defines a Coding column property for each non-mixture factor with a numeric data type. Coding Property Panel for Feed Rate shows the Coding column property panel for the column Feed Rate in the Reactor 20 Custom.jmp sample data table, found in the Design Experiment folder.
The Coding column property centers each value in a column by subtracting the midpoint of the High Value and Low Value. It then divides by half the range. Suppose that H is the High Value and L is the Low Value. Then every X in the column is transformed to the following:
The Reactor 20 Custom.jmp sample data table contains data from a 20-run design that was constructed using the Custom Design platform. The experiment investigates the effects of five factors on a yield response (Percent Reacted) for a chemical process.
1.
|
2.
|
3.
|
Open the Factors outline.
|
Notice that the settings for Temperature range from 140 to 180. When the design was generated, the Coding column property was assigned to Temperature. The Low Value is set to 140 and the High Value is set to 180.
5.
|
In the Reactor 20 Custom.jmp sample data table, click the asterisk next to Temperature in the columns panel and select Coding.
|
6.
|
Click Cancel to close the Column Info window.
|
7.
|
In the Reactor 20 Custom.jmp sample data table, select Run Script from the Reduced Model red triangle menu.
|
8.
|
Click Run.
|
In the Source list, the High and Low values used in the Coding column property appear in parentheses to the right of the main effects, Catalyst, Temperature, and Concentration. The ranges imposed by the Coding property are not shown for the interaction effects.
Tip: Notice the “^” symbols to the right of the PValues for Temperature and Concentration. These symbols indicate that these main effects are components of interaction effects with smaller p-values. If an interaction effect is included in the model, then the principle of effect heredity requires that all component effects are also in the model. See Effect Heredity in Starting Out with DOE.
9.
|
Select Estimates > Show Prediction Expression from the red triangle next to Response Percent Reacted.
|
Each factor is transformed as specified by the Coding column property. For example, for Temperature, notice the following:
‒
|
The Low Value in the Coding property was set to 140. The Temperature value of 140 is transformed to -1.
|
‒
|
The High Value in the Coding property was set to 180. The Temperature value of 180 is transformed to +1.
|
‒
|
The midpoint of the Low and High values is 160. The Temperature value of 160 is transformed to 0.
|
The transformed values help you compare the effects. The estimated coefficient for Catalyst is 9.942 and the estimated coefficient for Concentration is -3.077. It follows that the predicted effect of Catalyst on Percent Reacted is more than three times as large as the effect of Concentration on Percent Reacted. Also, the coefficients indicate that predicted Percent Reacted increases as Catalyst increases and decreases as Concentration increases.
•
|
When all factors are at their midpoints, their transformed values are 0. The predicted Percent Reacted is the intercept, which is 65.465.
|
•
|
When Catalyst and Concentration are at their midpoints, a 20 unit increase in Temperature increases the Percent Reacted by 5.558 units.
|
•
|
Suppose that Concentration is at its midpoint, so that its transformed value is 0:
|
‒
|
When Catalyst is at its midpoint, a 20 unit increase in Temperature increases the Percent Reacted by 5.558 units.
|
‒
|
When Catalyst is at its high setting, a 20 unit increase in Temperature increases the Percent Reacted by 5.558 + 6.035 = 11.593 units.
|
It follows that the coefficient of the interaction term, 6.035, is the increase in the slope of the model for predicted Percent Reacted for a 0.5 unit change in Catalyst.
The experimental data in the Tiretread.jmp sample data table results from an experiment to study the effects of SILICA, SILANE, and SULFUR on four measures of tire tread performance. In this example, you will consider only one of the responses, ABRASION.
1.
|
2.
|
Select Analyze > Fit Model.
|
3.
|
4.
|
5.
|
Check Keep dialog open.
|
6.
|
Click Run.
|
7.
|
The coefficients do not help you compare effect sizes. The sizes of the coefficients do not reflect the impact of the effects on ABRASION over the range of their settings. Also, the coefficients are not easily interpreted. For example, the coefficients do not facilitate your understanding of the predicted response when SILICA is at the midpoint of its range.
8.
|
In the Tiretread.jmp data table, select SILICA, SILANE, and SULFUR in the Columns panel. Right-click the highlighted area and select Standardize Attributes.
|
9.
|
Select Column Properties > Coding in the Standardize Properties panel.
|
10.
|
Click OK.
|
An asterisk appears in the Columns panel next to SILICA, SILANE, and SULFUR indicating that these have been assigned a column property.
11.
|
12.
|
The coefficients for the coded factors enable you to compare effect sizes. SILANE has the largest effect on ABRASION over the range of design settings. The effects of SILICA and the SILANE*SULFUR interaction are large as well.
The coefficients for the coded factors are also more easily interpreted. For example, when all factors are at the center of their ranges, the predicted value of ABRASION is the intercept, 139.12.
13.
|
Close the Tiretread.jmp sample data table without saving the changes.
|