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

Analyzing Central Composite Designs

Select the Model tab of the Analysis of a Central Composite (Response Surface) Experiment dialog box to access options to specify the terms to be included in the model.

Include in model

Use the options in the Include in model group box to determine which terms will be included in the model.

Linear main effects only

When the Linear main effects only option button is selected, the model will only contain linear main effects.

Lin./quad. main effects.

main effects. When the Lin./quad. main effects option button is selected, the model will only contain linear and quadratic main effects.

Linear main eff. + 2-ways.

When the Linear main eff. + 2-ways option button is selected, the model will include linear main effects and two-way interaction effects (for details, see also the Summary: Effect estimates option on the ANOVA/Effects tab).

Lin./quad. main eff. + 2-ways.

main eff. + 2-ways. When the Lin./quad. main eff. + 2-ways option button is selected, the model will include linear and quadratic main effects and two-way interaction effects.

Ignore some effects/Effects to ignore

Select the Ignore some effects check box or click the Effects to ignore button to display the Customized (pooled) error term dialog box, which contains a list of all factor effects and interactions in the current model. Highlight the factors or interactions that you want to ignore, that is, that you want to pool into the error term.

The first time that you click the Ignore some effects check box, a warning is displayed: After pooling effects, the ANOVA and multiple regression models (with original metric of variables) may no longer be the same (e.g., when you ignore lower-order but estimate higher-order effects).

Because of the recoding of factors involved in the computation of linear and quadratic main effects and interactions, the confounding of factor effects is different when you analyze the recoded factor settings as compared to the original factor settings; as a consequence, different effects may be statistically significant when you use the Summary: Effect estimates option versus the Regression coefficients option on the ANOVA/Effects tab. Thus, when you pool effects into the error term, then the model based on the original factor values may no longer be equivalent to the model based on the recoded factors. This will, for example, be the case when you choose to pool linear main effects, but not the quadratic components. You can always compare the mean-square-errors that are reported in the spreadsheet with the Summary: Effect estimates on the ANOVA/Effects tab and the spreadsheet with the Regression coefficients also on the ANOVA/Effects tab.

ANOVA error term

Depending on the model you have specified, two possible error terms can be used: SS residual or Pure error. The error term is used in all tests for statistical significance and in the computation of standard errors.

SS residual

If the SS residual option button is selected, the error term used for the ANOVA table and for computing the standard errors for the parameter estimates will be computed as the sum-of-squares residual for the dependent variable, after controlling for all effects in the current model.

Pure error

The Pure error option button is only available if at least some runs in the current design were replicated (see also the Introductory Overview). In that case, you can compute the variability of measurements within each unique combination of factor levels. That variability will give an indication of the random error in the measurements (e.g., due to uncontrolled factors, unreliability of the measurement instrument, etc.), because the replicated observations were taken under identical conditions (settings of factor levels). If you choose to use the estimate of Pure error for the error term, then the ANOVA table will also include a Lack of fit test (see Introductory Overview). This is a test of the residual variance, after controlling for all effects in the model, against the estimate of pure error. If significant, then there is indication of additional significant effects, or differences between means of the design that cannot be accounted for by the parameters currently in the model.

Model Profiler. Click this button to display the Model Profiler, where you can run simulations based on the specified model.