Analysis of an Experiment with Three-Level Factors - Model Tab

Analyzing the 3(k-p) Design

Select the Model tab of the Analysis of an Experiment with Three-Level Factors dialog box to access options to specify the terms to be included in the model.

Include in model

The options selected in the Include in model group box determine which terms will be included in the model. Note that the specified model will be applied to all selected dependent variables. All ANOVA results, effect estimates, predicted and residual values, etc., will be computed based on this model. See the note on Main Effects and Interactions for more details.

No interactions

When the No interactions option button is selected, the model will only contain main effects.

2-way interactions (linear x linear)

When the 2-way interactions (linear x linear) option button is selected, the model will include main effects and linear by (times) linear two-way interaction effects.

2-way interactions (linear, quadr)

When the 2-way interactions (linear, quadr) option button is selected, the model will include main effects and 1) linear by (times) linear, 2) linear by quadratic, 3) quadratic by linear, and 4) quadratic by quadratic 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 select 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 option Summary: Effect estimates versus option Regression coefficients 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 main effects and interactions and the spreadsheet with the regression coefficients.

ANOVA error term

Depending on the number of runs and/or replications in your design, you can choose between two error terms in the ANOVA error term group box. The selected error term will be used in all tests for statistical significance and in the computation of standard errors.

SS residual

If you select the SS residual option button, 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 Replicating the Design). 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.