ANOVA Tables for Mixture Experiments

Both the Quick tab and the ANOVA/Effects tab of the Analysis of a Mixture Experiment dialog box contain an ANOVA Table button. Click this button to produce two ANOVA tables for the current model, as specified in the Model group box.

Hierarchical model tests

The first spreadsheet contains results for hierarchical tests of different models of increasing complexity. For example, the spreadsheet may first show the results for the simple linear model (with df = q-1, for a design with q components). The next line will show the results of the next, more complex, model, i.e., the quadratic model (note that in these tests terms that were excluded by the user are ignored; see the check box Ignore some effects on the Model tab), and so on.

R-square

The ANOVA spreadsheet also reports the R-square values for the respective models. The R-square value can be interpreted as the proportion of variability around the mean for the dependent variable, that can be accounted for by the respective model. (Note that for non-intercept models, some multiple regression programs only compute the R-square value pertaining to the proportion of variance around 0 (zero) accounted for by the independent variables; for more information, see Kvålseth, 1985; OKunade, Chang, and Evans, 1993.)

Overall fit

The second spreadsheet shows the overall results for fitting the selected model.

Pure error and lack of fit

If at least some runs in the design where replicated, then the second 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.