Analysis of a Central Composite (Response Surface) Experiment - ANOVA/Effects Tab

Analyzing Central Composite Designs

Select the ANOVA/Effects tab of the Analysis of a Central Composite (Response Surface) Experiment dialog box to access options to review more detailed information about the ANOVA effects than available on the Quick tab. Note that these results are for the currently specified model. You can specify a new model via the Model tab.

Summary: Effect estimates

Click the Summary: Effect estimates button to produce a spreadsheet with the ANOVA effect estimates and coefficients of the model for the rescaled factor values (see the Review/set factor names and settings option on the Design tab). The effects that will be computed depend on the current model, as specified via the options in the Include in model group box on the Model tab. 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 value in the Confidence interval box (see below), and their statistical significance. Statistically significant parameters are highlighted in this spreadsheet; the criterion for statistical significance can be set via the Alpha (highlighting) option (see below, the default Alpha is .05). If the Effects sorted by size check box is selected (see below), the estimates in this spreadsheet will be sorted by their absolute size (except for the intercept, which is always listed first). For more information on the spreadsheet, see Main Effects and Interactions Spreadsheet for Central Composite Experiments.

Regression coefficients

Click the Regression coefficients button to compute the multiple regression estimates for the original factor values. The coefficients computed depend on the current model, as specified via the options in the Include in model group box on the Model tab. If an error term for the ANOVA is available, this spreadsheet will also include the standard errors of the regression coefficients, their confidence intervals (according to the value in the Confidence interval box, see below), and their statistical significance. Note that the ANOVA error term not only depends on the currently specified model, but also on the choice of error term in the ANOVA error term group box on the Model tab. Statistically significant parameters are highlighted in this spreadsheet; the criterion for statistical significance can be set via the Alpha (highlighting) option (see below, the default alpha is .05). If the Effects sorted by size check box is selected (see below), the estimates in this spreadsheet will be sorted by their absolute size (except for the intercept, which is always listed first).

Quadratic effects

To compute the quadratic effects, STATISTICA does not perform any recoding of factor values. For example, the quadratic main effects are computed by adding to the design (when computing the correlation matrix from which the regression coefficients are estimated) new variables that are set as equal to the squared original variable values (factor settings).

Effects sorted by size

Select the Effects sorted by size check box to review the Summary: Effect estimates as well as the Regression coefficients (see above) sorted by (absolute) size. This option is particularly useful in order to identify the important effects in a large design with many factors and interactions.

Confidence interval

The value in the Confidence interval box determines the confidence intervals that will be computed for all relevant options on this dialog. Confidence intervals for the parameter estimates are computed (if available) when you click the Summary: Effect estimations or Regression coefficients buttons (see above). Confidence intervals for the observed means (if replicate observations are available) are computed when you click the Display design and observed means button on the Design tab; confidence intervals for predicted values are computed when you click the Predict dependent variable values button on the Prediction & profiling tab.

Alpha (highlighting)

The value in the Alpha (highlighting) box determines the criterion for statistical significance for all relevant options on this dialog. When you click either the Summary: Main effects & interactions or Regression coefficients button (see above), this criterion is used for highlighting significant effects and coefficients in the resulting spreadsheets (if an error term is available). When you choose the Pareto chart of effects (and Plot standardized effects, see below), this criterion is used to draw a vertical line across the columns of the chart, to indicate the minimum magnitude for a significant effect.

ANOVA table

Click the ANOVA table button to produce the ANOVA table for the current model, as specified in the Include in model group box on the Model tab, and based on the chosen error term in the ANOVA error term group box on the Model tab. Refer to the note on Main Effects and Interactions for a detailed discussion of the different effects and the coding of the blocking variables.

Pure error and lack of fit

Note that if you select the estimate of Pure error for the error term via the Model tab (if it was 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, 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.

Plots of effects

Use the options in the Plots of effects group box to review plots for the current model and to specify criteria for the plots.

Normal probability plot

Click the Normal probability plot button to produce a normal probability plot of the ANOVA parameter estimates for the current model (as specified in the Include in model group box on the Model tab). In this plot, the normal probabilities of the rank-ordered parameters are plotted on the y-axis, and the actual parameter estimates (optionally standardized) are plotted on the x-axis. If all estimates come from a population with a mean parameter estimate of zero and a common variance, then the points in this plot will approximate a straight line. "Real" effects will show in this plot as outliers. To summarize, this plot helps you distinguish between random noise and real effects.

Half-normal probability plot

Click the Half-normal probability plot to produce a half-normal probability plot of the ANOVA parameter estimates for the current model (as specified in the Include in model group box on the Model tab).

Pareto chart

Click the Pareto chart 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, see below). The Pareto chart shows the effect estimates sorted by their absolute size. If you plot the standardized effects, then 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 (see above). 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.

Label points in normal plot

If the Label points in normal plot check box is selected, the points in the normal probability plot of effects will be labeled.

Exclude block effects

If the current design contains blocking, select the Exclude block effects check box to omit the block effects from the Pareto chart of effects or the Normal probability plot of effects. Note that this option is only available if the current design contains blocking.

Plot standardized effects

If the Plot standardized effects check box is selected, the Pareto chart of effects and the probability plot of effects will be produced for the standardized effects, that is, for the effects divided by their respective standard errors. Note that this option is only available if the standard error for the parameter estimates can be computed. Also, the standard errors are dependent on the current model and choice of error term (see Main Effects and Interactions, for details).