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

Analyzing Central Composite Designs

Select the Quick tab of the Analysis of a Central Composite (Response Surface) Experiment dialog box to access options to quickly compute analysis results. Note that these results are for the currently specified model. You can specify a new model via the Model tab.

Summary: Effect estimates

Click the Summary: Effect estimates button to produce a spreadsheet with the ANOVA effect estimates and coefficients of the model for the rescaled factor values (see Review/set factor names and settings on the Design tab). The effects that are computed depend on the current model, as specified via the options in the Include in model group box on the Model tab. If an error term for the ANOVA is available, this spreadsheet also includes the standard errors of the parameter estimates and coefficients, their confidence intervals (according to the value in the Confidence interval box on the ANOVA/Effects tab, and their statistical significance. Statistically significant parameters are highlighted in the spreadsheet; the criterion for statistical significance can be set via the Alpha (highlighting) option on the ANOVA/Effects tab (the default Alpha is .05). If the Effects sorted by size check box on the ANOVA/Effects tab is selected, the estimates in the spreadsheet are sorted by their absolute size (except for the intercept, which is always listed first). For more information on the spreadsheet, see Main Effects and Interactions Spreadsheet for Central Composite Experiments.

ANOVA table

Click the ANOVA table button to produce the ANOVA table for the current model, as specified in the Include in model group box on the Model tab, and based on the selected error term in the ANOVA error term group box on the Model tab. Refer to Main Effects and Interactions for a detailed discussion of the different effects and the coding of the blocking variables. Options for using pure error for the error term are available on the ANOVA\Effects tab.

Pareto chart of effects

Click the Pareto chart of effects button to produce a Pareto chart of the ANOVA effect estimates, or, optionally, the standardized effect estimates (if the Plot standardized effects check box is selected on the ANOVA/Effects tab). The Pareto chart shows the effect estimates sorted by their absolute size. If you plot the standardized effects, then a vertical line is also shown to indicate the minimum magnitude of statistically significant effects, given the current model and choice of error term, and using the criterion of statistical significance entered in the Alpha (highlighting) box on the ANOVA/Effects tab. The Pareto chart is very useful for reviewing a large number of factors and for presenting the results of an experiment to an audience that is not familiar with standard statistical terminology.

Fitted response surface. Click the Fitted response surface button to display the currently fitted model in a surface plot, along with the observed points in the experiment. Additional options for this plot are available on the Prediction & profiling tab. Note that the parameters shown in this function pertain to the regression coefficients, that is, to the factor settings in their original metric (see also the Summary: Effect estimates and Regression coefficients options on the ANOVA/Effects tab for additional details). Thus, this surface will always show the predicted values for the dependent variable, given the original factor settings. Also see the note on Additional factors and blocking variables below.

Fitted response profiles

Click the Fitted response profiles button to display the currently fitted model in a contour plot, along with the observed points in the experiment. Additional options for this plot are available on the Prediction & profiling tab. Note that the parameters shown in this function pertain to the regression coefficients, that is, to the factor settings in their original metric (see also the Summary: Effect estimates and Regression coefficients options on the ANOVA/Effects tab for additional details). Thus, this surface will always show the predicted values for the dependent variable, given the original factor settings. Also see the note on Additional factors and blocking variables below.

Note: Additional factors and blocking variables. If there are more than two factors in the current design, you will be prompted to select the two variables for the surface or contour plot in the Select factors for 3D plot dialog box. Additionally, when there are more than two factors in the current experiment and/or there are blocks included in the current model, you can specify the values for those additional factors, for which to compute the surface or surface contours (i.e., for which to compute the fitted values) in the Select factor values dialog box. Remember that the block effects are computed from added (to the design) coded variables. The coding for those effects is described in the Main Effects and Interactions topic.

Critical values (min, max, saddle)

Click the Critical values button to produce three spreadsheets that provide results of the analysis of the quadratic response surface. For a description of these spreadsheets, see Critical Values Spreadsheets for Central Composite Designs. The Critical values button is only available when a standard quadratic response surface model is used to predict the dependent variable, i.e., it is available only when the current model (as specified via the options in the Include in model group box on the Model tab) includes all linear and quadratic main effects and, if it includes interaction effects, it includes all linear-by-linear interaction effects; hence, this option will not be available if you choose to Ignore some effects (specify a custom model), or if the current model includes quadratic-by-quadratic interactions (in a design where all factors have 3 levels). See Main Effects and Interactions for additional details regarding the models that can be specified.