Analysis of an Experiment with Three-Level Factors - Prediction & Profiling Tab
Analyzing the 3(k-p) Design
Select the Prediction & profiling tab of the Analysis of an Experiment with Three-Level Factors dialog to access options to generate plots for the fitted response surface and predicted values as well as to perform response desirability profiling. Note that these results are for the currently specified model. You can specify a new model on the Model tab.
- Response desirability profiling
- Click the Response desirability profiling button to display the
Profiler dialog. Use the Profiler to inspect the predicted values for the dependent variables at different combinations of levels of the independent variables, to specify desirability functions for the dependent variables, and to specify a search for the levels of the independent variables that produce the most desirable response on the dependent variables.
Surface plot (fitted response). Click the Surface plot (fitted response) button to plot the currently fitted model in a surface plot, along with the observed points in the experiment. If there are more than two factors in the current design, the Select factors for 3D plot dialog is displayed when you click the Surface plot (fitted response) button. From this dialog, select the two variables for the plot.
When there are more than two factors in the current experiment and/or there are block effects included in the current model, the Select factor values dialog also is displayed, in which you specify the values for those additional factors, for which to compute the surface plot (i.e., for which to compute the fitted values). Remember that the block effects are computed from added (to the design) coded variables. The coding for those effects is described in the description of Main effects and interactions.
If the Show fitted function check box is selected (see below), the plot will also contain, as custom text, the currently fitted function (model). 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 options Summary: Effect estimates and Regression coefficients 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.
- Contour plot (fitted response)
- Click the Contour plot (fitted response) button to plot the currently fitted model in a contour plot, along with the observed points in the experiment. If there are more than two factors in the current design, the
Select factors for 3D plot dialog is displayed when you click the Surface plot (fitted response) button. From this dialog, select the two variables for the plot.
When there are more than two factors in the current experiment and/or there are block effects included in the current model, the Select factor values dialog also is displayed, in which you specify the values for those additional factors, for which to compute the surface plot (i.e., for which to compute the fitted values). Remember that the block effects are computed from added (to the design) coded variables. The coding for those effects is described in the description of Main Effects and Interactions.
If the Show fitted function check box is selected (see below), the plot will also contain, as custom text, the currently fitted function (model). 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 options Summary: Effect estimates and Regression coefficients 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.
- Show fitted function
- If the Show fitted function check box is selected, then the surface or contour plot will include, as custom text, the currently fitted function. Note that you can edit this text in the usual manner, as described in Graph Options dialog - Custom function.
- Show area contours
- If the Show area contours check box is selected, then the contours in the contour plot will be area (filled) contours; otherwise the surface contours will be indicated by lines.
- Critical values, minimum, maximum
- Click the Critical values, minimum, maximum button to display three spreadsheets that provide results of the analysis of the quadratic response surface. For a description of these spreadsheets, see Critical Values for Experiments with Three-Level Factors. The Critical values, minimum, maximum 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 also option Summary: Effect estimates on the ANOVA/Effects tab for additional details regarding the models that can be specified.
- Predicted vs. observed values.
- Click the Predicted vs. observed values button to display a scatterplot of the predicted values (given the current model) versus the observed values for the dependent variable.
- Predict dependent variable values
- Use this option to compute predicted values for the dependent variable, based on values for the factors that you define, and based on the current model as specified in the Include in model group box on the Model tab. Click the Predict dependent variable values button to display the Select factor values dialog. The values should be specified here in terms of the original factor metric, not in terms of the recoded (to ±1) factor values (for additional details, see option Summary: Effect estimates and Regression coefficients on the ANOVA/Effects tab). After specifying the factor values from which to compute the predicted value, a spreadsheet is displayed with the results. If available, the spreadsheet will also display the confidence interval for the respective predicted value. Those confidence limits are computed from the current ANOVA error term, and the percentile value specified in the Confidence interval box on the ANOVA/Effects tab.
- Block effects
- If the current model contains block effects, then you can also specify values for those (added to the design) block variables. The coding (and thus interpretation) for those effects are described in Main Effects and Interactions for Experiments with Three-Level Factors.