Design & Analysis of Central Composite (Response Surface) Experiments - Analyze Design Tab
Select the Analyze design tab of the Design & Analysis of Central Composite (Response Surface) Experiment dialog box to access options to specify the variables to use in analyzing a central composite (response surface) experiment.
The central composite design analysis options do not make any assumptions about the structure of your data file, that is, the number of distinct factor values, or their combinations across the runs of the experiment. Hence, these options can be used to analyze any type of (non-mixture) design, to fit to the data the general model of the type:
y = b0 + b1*x1 +...+ bk*xk + b12*x1*x2 + b13*x1*x3 +...+ bk-1*xk*xk-1 + b11*x12 +...+ bkk *xk2
where xi stands for the factor values for factor i, and y stands for the dependent variable values. For more details concerning these types of designs, refer to the Introductory Overview.
- Variables
- Click the Variables button to display a standard variable selection dialog box, in which you specify the dependent variables of interest, the independent variable list (list of factors in the design), and an optional blocking variable.
Note: Multiple dependent variables and missing data. When more than one dependent variable is specified, Statistica performs casewise deletion of missing data when reading the data. Thus, a case or run is excluded from the analysis if it has missing data for any of the dependent variables specified for the analysis.
- To recode factor values (levels), use
- Use the options in the To recode factor values (levels), use group box to determine how the values for each factor will be rescaled, that is, how the lowx and highx values in the formula (see below) will be determined.
Ordinarily, when analyzing standard central composite designs, you want to rescale the original factor values so that the low and high factor settings for each factor are transformed to -1 and +1, respectively. Specifically, the values x for a factor would be transformed to x' via:
x' = (x - averagex)/[1/2 * (highx - lowx)]
This 1) enables you later to interpret the effect estimates in the standard manner (i.e., as the differences between the respective factors' low and high settings), and 2) makes the effect estimates (and coefficients) for different factors comparable in size (see Analysis of a Central Composite (Response Surface) Experiment; however, remember that regardless of scaling, this dialog box also always allows you to review the regression coefficients for the original factor settings.
- Automatically determined factor levels from file
- If the Automatically determined factor levels from file option button is selected, Statistica automatically determines the values for lowx and highx from the values found in the data file. The specific values that are selected depends on how many distinct values are found in the data file: 1) If there are 2 distinct values or settings for a factor, they will be used as low and high in the rescaling of factors; 2) if there are 3 distinct values, the smallest of the 3 will be taken as the low value, and the largest of the 3 will be taken as the high value; 3) if there are 5 distinct values, the most extreme values are interpreted as star-point values (of a central composite design), and the next-to-the-most-extreme values are taken as the low and high values; 4) if there are exactly 4 distinct values, or more than 5 levels, Statistica automatically switches to the User-defined values method (see below). This method of determining the low and high values automatically identifies the appropriate (for later analyses) low and high factor settings for standard 2(k-p) designs, with or without center points, 3(k-p) and Box-Behnken designs, designs for 2 and 3 level factors, and for central composite designs.
- User-defined high/low factor values
- When you select the User-defined high/low factor values option button (or click the adjacent
button), Statistica first reads the data to determine default values for lowx and highx as described above, and then produces the
Factor Levels for Recoding Factor Values spreadsheet containing the values. You can then modify the low and high values for each factor. Click the OK button to accept the Low and High values in the first two numeric columns and return to the
Design & Analysis of Central Composite (Response Surface) Experiments dialog box. See also General User Entry Spreadsheet. Note that you can later modify the low and high factors settings that are used for recoding the factor values on the
Analysis of a Central Composite (Response Surface) Experiment - Design tab.
Note: Adding customized terms to the model. Because you can later select individual factors and interactions that are to be included in the model (on the Analysis of a Central Composite (Response Surface) Experiment dialog box), you can include factors or variables that were computed (e.g., via spreadsheet formulas) as combinations of other factors. Thus, via these options, you can include in the fitted model higher order interactions, cubic or quadratic terms, etc.Note: central composite (response surface) designs can also be analyzed via General Linear Models (GLM) or General Regression Models (GRM), or via the (nonlinear) Generalized Linear/Nonlinear Models (GLZ) options.See also Example 5: Central Composite (Response Surface) Designs.