Point Prediction

This screen provides the mean model predictions for all fitted responses, along with their confidence and tolerance intervals (CI and TI; respectively)—plus other statistics. (Looking for the prediction interval (PI) on one or more runs at a one or more specified factor location? If so, go to the Confirmation node.) Generally, this will be done after Numerical optimization sets the factors to the number 1 solution. However, other locations can be established via the Factors tab.

Details on the Point Prediction table:

  • If a location lines up with an actual run, the Observed response will display.

  • If the Std. Dev. is not zero, then factor variability was added to the factor information and will be used to estimate propagated error (POE).

  • 95% CI (confidence interval) range: 95% of confidence intervals generated from similar independent experiments will contain the true average outcome for the current factor settings.

  • 95% TI (tolerance interval) range: 95% of tolerance intervals generated from similar independent experiments will contain 99% of all future observations for the current factor settings. The TI, by it including all future individual outcomes, will always be wider than the CI, which operates on the mean response.

  • The Confidence level can be changed by using the Edit, Preferences menu and going to the Math Analysis section. The significance threshold (default 0.05) and the tolerance level can be adjusted (default 99%).

  • The reported intervals do not include variation from block effects.

  • When standard deviation is entered for one or more factors, this variation inflates the Std Dev, SE Mean and intervals in a second line labeled “POE” (propagation of error).

  • Though not recommended due to dangers of extrapolation, predictions are provided for numeric process factors set outside their experimental range (Mixture components require special treatment due to constraints on their total.) This feature is useful for considering an expansion of the current design space.

If a transformation is applied during analysis the model is predicting the median rather than the mean in the original scale. The predicted mean and median will differ when presented in the original scale.

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  • G.W. Oehlert. A note on the delta method. American Statistician, 46:27–29, 1992.