 # ANOVA with Center Points¶

The ANOVA is where the descriptive statistics and statistical tests are presented. In general, look for low p-values to identify important terms in the model.

Select View > Annotated ANOVA to see the annotation text to help interpret the key elements in the ANOVA report.

Right-click in a cell on the report and select Help from the menu for details about that section.

This style of ANOVA is used for factorial designs that include center points. The main difference between this ANOVA and the standard ANOVA is that it includes a formal test for curvature in the center of the design space.

The data can be viewed in two ways:

• With curvature term (default): Fits a model that adjusts for the effects of the center points and tests if there is curvature in the center of the design space.

• Without curvature term: Fits the ordinary regression model to the data

## ANOVA Sections¶

Curvature Test: Due to the presence of center points, a formal check for curvature can be made.

• With Curvature Term: This is the adjusted model, which adds a categoric curvature term to the model. By default, this curvature term is included in the model. The curvature term is tested for significance in the Curvature Check pane. If the curvature term is not significant, it can be removed from the model, which will remove the Curvature Check pane from the ANOVA. If the curvature is significant, considering augmenting the factorial design to a response surface design. Click here for more information.

• Without Curvature Term: This is the unadjusted model, which is simply the ordinary regression model. The center points are treated the same as the other factorial points in the model.

The curvature term can be included/excluded from the model by clicking the Add Curvature Term or Remove Curvature Term Button.

Note

If the curvature term is in the model, all remaining output, diagnostics, and graphs will be adjusted to included the curvature term. If the curvature term is excluded from the model, all output, diagnostics, and graphs will not be adjusted for the curvature term.

ANOVA: This is the standard ANOVA.

Fit Statistics: The descriptive statistics are used as a secondary check for the usefulness of the model.

• Subtract the Predicted R-Squared from the Adjusted R-squared. If the difference is less than 0.2, then the model is fitting the data and can reliably be used to interpolate.

• Check the Adequate Precision. If it is greater than 4, then the model has a strong enough signal to be used for optimization.

• CV% is used in some industries to judge the capability of a process; lower is better.

• Compare the standard deviation to the estimate used when sizing the design (power or FDS).

• The mean is the average of the response, and the PRESS is used to calculate other statistics such as the predicted R-squared.

• Likelihood statistics (including BIC and AICc) can be used to compare models.

Coefficients: This section provides the confidence intervals around the estimated model coefficients. While most analyses do not require examining these intervals, they can help sort out issues when the analysis doesn’t make sense.

Equations: As many as two model equations will be presented. One for the coded model taken from the coefficient table above, and one for the actual model which is rescaled to include the factor units of measure.