Analysis of a Central Composite (Response Surface) Experiment - Design Tab

Analyzing Central Composite Designs

Select the Design tab of the Analysis of a Central Composite (Response Surface) Experiment dialog box to access options to view various aspects of the central composite experiment. Note that these results are for the currently specified model. You can specify a new model via the Model tab.

Display design and observed means

Click the Display design and observed means button to produce a spreadsheet showing the unique runs (those with unique combinations of factor settings) in the experiment. In addition, for each unique run STATISTICA computes the mean, standard deviation, and standard error of the mean (if there is more than one run for the respective unique combination of factor settings).

Show text labels instead of factor values

If the Show text labels instead of factor values check box is selected, the factor settings in the spreadsheet are identified by their respective text labels. Note that this button is not available if there are no text labels in the file (for the list of independent variables or factors).

Review/set factor names and settings

Click the Review/set factor names and settings button to display the Factor Levels for Recoding Factor Values spreadsheet, which contains the factor low and high settings (see also General User Entry Spreadsheet). These values are used to transform the original factor values in the computation of the Summary: Effect estimates on the ANOVA/Effects tab, and also in the computation of the Correlation matrix of design variables and Correlations of effects (see below). To change the default values (see also the Design & Analysis of Central Composite (Response Surface) Experiments - Analyze Design tab), enter the respective values in the Low Value and High Value columns of the spreadsheet and then click the OK button.

Usually, 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 to interpret the effect estimates in the standard manner (i.e., as the differences between the respective factors' low and high settings, see also the Summary: Effect estimates option on the ANOVA/Effects tab), and 2) makes the effect estimates (and coefficients) for different factors comparable in size. (Note that, regardless of scaling, the Regression coefficients option on the ANOVA/Effects tab will always show the coefficients for the original factor settings.)

The options in the box labeled To recode factor values (levels), use will determine how the values for each factor will be rescaled, that is, how the lowx and highx values in the formula shown above will be determined.

Corr. matrix of design variables (X'X).

Click the Corr. matrix of design variables (X'X) button to produce a correlation matrix for the columns of the current design matrix. Thus, the number of effects displayed in this matrix depends on the current choice of the model in the Include in model group box on the Model tab. The correlations for the linear main effect vectors are computed from the rescaled factor values (see Review/set factor names and settings above); the correlations for the quadratic main effect vectors are computed from the squared linear main effect vectors; the correlations for the interaction effect vectors are obtained by multiplying out the respective linear main effect vectors or columns. The correlations in this matrix reflect on the redundancy of the respective effects. To aid in the review of this matrix, all correlations that are not equal to 0.0 are highlighted in the matrix.

Correlation of effects (X'X inverse)

Click the Correlation of effects (X'X inverse) button to produce the standardized inverse of the correlation matrix described in the previous paragraph. This matrix can be interpreted as the correlation matrix of effects; that is, it is the standardized variance/covariance matrix of the parameter estimates for the current model. The greater the absolute value of a correlation between effects in this matrix, the more redundant are the respective effects. To aid in the review of this matrix, all correlations that are not equal to 0.0 are highlighted in the matrix. Also, note that the Display matrices in compressed format option (see below) applies to this spreadsheet as well.

Display matrices in compressed format

If the Display matrices in compressed format check box is selected, the width for the columns in the spreadsheet with the correlations will be set to 4 (4 characters, including the decimal point, will show in each cell of the correlation matrix, e.g., value 0.31). This compressed format allows you to review large matrices efficiently. Clear the Display matrices in compressed format check box to display the cells in the spreadsheet in the usual default width of 8 characters per cell (e.g., to display 0.312345). Of course, you can always use the standard spreadsheet option Format - Cells to change the display format for the spreadsheet; remember that, regardless of display format, values in spreadsheets are always stored in their highest precision.