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

Analyzing the 3(k-p) Design

Select the Quick tab of the Analysis of an Experiment with Three-Level Factors dialog box to access options to quickly review the results of your analysis. Note that these results are for the currently specified model. You can specify a new model on the Model tab.

Summary: Effect estimates

Click the Summary: Effect estimates button to produce a spreadsheet with the ANOVA effect estimates and coefficients for the coded model. The effects that are computed depend on the current model, as specified via the options in the Include in model group box on the Model tab, and on the recoding of the factor values (i.e., the parameterization of the model) as indicated via option Use centered and scaled polynomials described below. If an error term for the ANOVA is available, this spreadsheet will also include the standard errors of the parameter estimates and coefficients, their confidence intervals (according to the setting of the Confidence interval box on the ANOVA/Effects tab), and their statistical significance. Additional options for Alpha highlighting and sorting effects are available on the ANOVA/Effects tab.

All estimates in this spreadsheet pertain to the coded factor settings, that is, to the factor settings scaled to the ±1 range (see also option Use centered and scaled polynomials, described below). To see the results for the original (untransformed) factor settings, use option Regression coefficients on the ANOVA/Effects tab. See Main Effects and Interactions for Experiments with Three-Level Factors for a detailed description of this spreadsheet.

ANOVA table

Click the ANOVA table button to produce two ANOVA tables (see ANOVA Tables for Experiments with Three-Level Factors for more details) for the current model, as specified in the Include in model group box and based on the chosen error term in the ANOVA error term group box, both on the Model tab, and based on the parameterization that follows from the setting of the Use centered and scaled polynomials check box. Refer to the description of the Main Effects and Interactions spreadsheet for a detailed discussion of the different effects, the coding of the blocking variables, and the effect of clearing the (default) Use centered and scaled polynomials option.

Pure error and lack-of-fit

Note that if you chose to use the estimate of Pure error for the error term via the Model tab (if it is available), 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. For example, there may be higher-order interactions between the factors in the design.

Pareto chart of effects

Click the Pareto chart of effects button to produce a Pareto chart of the ANOVA effect estimates, or, optionally, the standardized effect estimates (if the Plot standardized effects check box is selected on the ANOVA/Effects tab). The Pareto chart shows the effect estimates sorted by their absolute size. If you plot the standardized effects, a vertical line will also be shown to indicate the minimum magnitude of statistically significant effects, given the current model and choice of error term, and using the criterion of statistical significance selected in the Alpha (highlighting) box on the ANOVA/Effects tab. The Pareto chart is very useful for reviewing a large number of factors, and for presenting the results of an experiment to an audience that is not familiar with standard statistical terminology.

Use centered & scaled polynomial

When the Use centered & scaled polynomial check box is selected (the default), the original factor settings are recoded so that the effect estimates are comparable in size to the linear main effect estimates. When this check box is cleared, the coding for the quadratic main effects is the result of squaring the ±1 coding for the linear main effects. In that case, the effect estimates are not comparable in size to the linear effect estimates.

Observed marginal means

Use the options in the Observed marginal means group box to display the marginal means for the current model.

Display

Click the Display button to display the Compute marginal means for dialog box, in which you specify for which factors to display marginal means. Specify the factors and click the OK button to compute the marginal means for the design (e.g., the means for Factor 1 by Factor 2, collapsed across Factor 3 and Factor 4) and display them in a spreadsheet. If the Show text labels instead of factor values check box is selected on the Design tab, the factor levels in this spreadsheet are labeled with their text labels.

Means plot

Click the Means Plot button to produce a plot of weighted or unweighted marginal means. First, the Compute marginal means for dialog box is displayed, in which you specify for which factors to display marginal means. After selecting the factors, the Specify the arrangement of the factors in the plot dialog box is displayed, in which you select the assignment of factors. Note that the orientation and layout of the x-upper value labels can be adjusted via the Graph Options dialog box. If the Show text labels instead of factor values check box is selected on the Design tab, factor levels in this plot will be labeled with the respective text labels. The computation of the marginal means, standard errors, and confidence intervals follows the procedures outlined in the note on Marginal Means.

Display/plot weighted means

Select the Display/plot weighted means check box to display or plot weighted marginal means. For more details, see Marginal Means in Experiments with Three-Level Factors.

Predicted (estimated) response.

Surface plot of fitted response

Click the Surface plot of fitted response button to plot the currently fitted model in a surface plot, along with the observed points in the experiment. If the Show fitted function check box is selected on the Prediction & profiling tab, 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.

Select factors for 3D plot

If there are more than two factors in the current design, after you click the Surface plot of fitted response button, the Select factors for 3D plot dialog box is displayed, where you select the two variables for the surface plot.

Select factor values

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 box is displayed, in which you specify the values for those additional factors, for which to compute the surface (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 Main effects and interactions.

Critical values, minimum, maximum

Click this button to produce 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 (above) for additional details regarding the models that can be specified.