Main Effects and Interactions for Central Composite Experiments

Both the Quick tab and the ANOVA/Effects tab of the Analysis of a Central Composite (Response Surface) Experiment dialog box contain the Summary: Effect estimates button. Click this button to produce a spreadsheet with the ANOVA effect estimates and coefficients of the model for the rescaled factor values. If an error term for the ANOVA is available, this spreadsheet will also include standard errors of the parameter estimates and coefficients, their confidence intervals, and their statistical significance.

Mean/Intercept

The row labeled Mean/Interc. contains the estimate of the intercept for the regression model, based the rescaled factor settings (see also Multiple Regression).

Block effects

The block effects are computed from recoded added (to the design) variables, one for each degree of freedom. For example, if you have 4 blocks in the design then 3 new variables are created to exploit the 3 degrees of freedom associated with the overall block effect. Specifically, each new variable bi is computed as:

bi = -1	if block = 1
1	if block = i+1
0	otherwise

Linear main effects

The values shown in the column labeled Effect, and in the rows labeled by the main effects, are the ANOVA effect estimates. These can be interpreted as the differences (for the dependent variable) between the low settings and the high settings for the respective factors (see also the Review/set factor names and settings button on the Design tab). The values shown in the column labeled Coeff. are the regression coefficients for the coded model, and they can be interpreted as the differences between the high factor settings and the averages of the low and high factor settings for the respective factors. Thus, they are half the size of the Effect estimates.

Quadratic main effects

The values shown in the column labeled Effect, and in the rows containing the factor names followed by (Q), are the estimates for the quadratic main effects. The values shown in the Coeff. column are the respective regression coefficients, which are half the size of the Effects.

Linear by linear interaction effects

The values in the Effect column, in the rows denoting the linear factor interaction effects, are computed as twice the coefficients (shown in the Coeff. column) for the interactions. The coefficients are the regression coefficients for the product of the rescaled factor values.

Standard error of parameter estimates

The standard errors for the parameter estimates (ANOVA estimates and coefficients) are computed from the current ANOVA error term, as selected in the ANOVA error term box, and depending on the model as specified in the Include in model group box on the Model tab.