Analysis of a Mixture Experiment - ANOVA/Effects Tab

Select the ANOVA/Effects tab of the Analysis of a Mixture Experiment dialog 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: Estimates, pseudo-components

Click the Summary: Estimates, pseudo-components button to display a spreadsheet with the parameter (coefficient) estimates for the current model based on the transformed pseudo-components. The effects computed depend on the current model, as specified via the options on the Model tab. If a residual variance estimate is available, the spreadsheet will also include the standard errors of the parameter estimates, their confidence intervals (according to 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) box (the default Alpha is .05, see below). If the Effects sorted by size check box is selected, the estimates in this spreadsheet will be sorted by their absolute size.

All estimates in this spreadsheet pertain to the rescaled factor settings; that is, to pseudo-components. To see the results for the original (untransformed) factor settings, use the Estimates, original components option (see below). Note that if your original components were already scaled to the standard 0-1 range (and the mixture total is equal to 1.0), then the Estimates, original components option button is not available, and the results shown for this option are identical to those for the original components (because the pseudo-component transformation will not change the factor values in that case; see the formula in Estimates, Pseudo-Components in Mixture Experiments).

Estimates, original comps

Click the Estimates, original comps button to display a spreadsheet with the coefficient estimates for the original (untransformed) component values. The coefficients computed depend on the current model, as specified via the options on the Model tab. If a residual variance estimate is available, this spreadsheet will also include the standard errors of the coefficients, their confidence intervals (according to the setting of the Confidence interval box, see below), and their statistical significance. Statistically significant parameters are highlighted in the spreadsheet; the criterion for statistical significance can be set via the Alpha (highlighting) box (the default alpha is .05, see below). If the Effects sorted by size check box is selected (see below), the estimates in this spreadsheet will be sorted by their absolute size. Note that the statistical significance (if computed) for the main effect coefficients must be interpreted with caution. Because of the general mixture constraint (sum of component values must be constant), there are only q-1 degrees of freedom associated with the q components. Note that the Estimates, original comps option button is only available if the current component settings are not proportions in the standard 0-1 range; otherwise, the pseudo-component transformation will not affect the component values, and the results for the original component values will be the same as those reported for the pseudo-components.

Effects sorted by size

Select the Effects sorted by size check box to review the Estimates (for pseudo-components and original component values) 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 to be computed for all relevant options on this dialog. Confidence intervals for the coefficient estimates are computed (if available) when you click the Summary: Estimates, pseudo-components or Estimates, original comps buttons. 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 Display Design tab; confidence intervals for predicted values are 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 on this dialog. When you click the Summary: Estimates, pseudo-components or Estimates, original components (see above), this criterion is used for highlighting significant effects and coefficients. When you click the Pareto chart of effects button (and Plot standardized effects, see below), this criterion will be 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 two ANOVA tables for the current model, as specified on the Model tab. For a description of the two tables, see ANOVA Tables for Mixture Experiments.

Plots of effects

Use the Plots of effects group box to access the options described here.

Normal probability plot

Click the Normal probability plot button to display a normal probability plot of the coefficient estimates for the current model (as specified 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 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 button to display a half-normal probability plot of the coefficient estimates for the current model (as specified on the Model tab).

Pareto chart of effects

Click the Pareto chart of effects button to display a Pareto chart of the coefficient estimates for the current model. The Pareto chart shows the effect estimates sorted by their absolute size. If you plot the standardized effects, then a vertical line is also 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 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 plots

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

Plot standardized effects

If the Plot standardized effects check box is selected, then 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 the Plot standardized effects check box is only available if the standard error for the parameter estimates can be computed.

Plot original components

If the Plot original components check box is selected, then the normal plot of coefficients and the Pareto chart will be produced for the coefficients estimated for the original (untransformed) components (and not for the coefficients pertaining to the pseudo-components). Please refer to options Summary: Estimates, pseudo-components and Estimates, original components above for additional details.