Analysis of an Experiment with Two-Level Factors - ANOVA/Effects Tab

Analyzing the Results of a 2(k-p) Experiment

Select the ANOVA/Effects tab in the Analysis of an Experiment with Two-Level Factors dialog box to access options to review more detailed information about the ANOVA effects than those available on the Quick tab. Note that these results are for the currently specified model. You can specify a new model on the Model tab.

Summary: Effect estimates

Click this button to produce a spreadsheet with the ANOVA effect estimates and coefficients for the coded model. 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, see below), and their statistical significance. Statistically significant parameters will be highlighted in this spreadsheet; the criterion for statistical significance can be set via the Alpha (highlighting) option (the default alpha is .05, see below). All estimates in this spreadsheet pertain to the coded factor settings, that is, to the factor settings scaled to the ±1 range. To see the results for the original (untransformed) factor settings, click the Regression coefficients button (see below). For a description of the statistics given in this spreadsheet, see Main Effects and Interactions for Experiments with Two-Level Factors.

Regression coefficients

Click this button to display 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 setting of 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.

Effects sorted by size

Select this check box to review the Summary: Effect estimates and the Regression coefficients sorted by (absolute) size (except for the intercept, which is always listed first). 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 field 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 estimates button or the Regression coefficients buttons on this tab. Confidence intervals for the observed means (if replicate observations are available) will be computed when you click the Display design and observed means button on the Design tab. Confidence intervals for marginal means will be computed if you choose the Marginal means options (spreadsheet or plot) on the Means tab. Confidence intervals for predicted means are computed when you click the Square or Cube plot buttons on the Quick tab or Means tab. Confidence intervals for predicted values will be computed when you click the Predict dependent variable values button on the Prediction and Profiling tab.

Alpha (highlighting)

The value in the Alpha (highlighting) box determines the criterion for statistical significance for all relevant options in this dialog box. The default Alpha is .05. When you click the Summary: Effect estimates button or the Regression coefficients buttons on this tab, this criterion is used for highlighting significant effects and coefficients (if an error term is available). When you click the Pareto chart button (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 display an ANOVA table for the current model, as specified in the Include in model group box and based on the selected error term in the ANOVA error term group box, both on the Model tab. Note that if you selected to use the estimate of Pure error for the error term (if it was available), the ANOVA table will also include a Lack of fit test (see the 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 create the plots described here and to specify special effects.

Normal probability plot of effects

Click the Normal probability plot of effects 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, 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 of effects

Click this button 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 (select the Plot standardized effects check box, see below), 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

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

Exclude block effects

When 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

When this 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).