Analysing your Results (Fit Summary & Model)

 

Under Analysis on the left-hand tree structure, click on each response you want to analyse and simply work your way along the analysis buttons from left-to-right. For the Transform, start with None and proceed to the next button. You may wish to reconsider a transformation after examining the Diagnostics.

Fit Summary: uses 3 tables of statistics to recommend the complexity or order of Model to fit to your data…

 

 

• Sequential Model Sum of Squares chooses the highest order of polynomial model required to significantly explain the variability in your data
• Lack of Fit Tests compares the model’s residual error to the pure error from the replicated design points to recommend the model with insignificant lack of fit
• Model Summary Statistics suggests the simplest model which both explains and predicts the greatest fraction of variation in the data; using the Adjusted R-Squared and Predicted R-Squared statistics respectively

Warning: Design Expert considers all the terms which make up the order of each polynomial model, however insignificant, to recommend the complexity of the model that best fits your data. The Quadratic model listed in the example above will include all main effects, all two factor interactions and all squared terms when only a subset of these would be necessary. For less experienced users we recommend you follow the steps outlined in the next section under Model, regardless of the model recommended under Fit Summary. Also, don’t worry about the WARNING message as it is simply letting you know if the design isn’t capable of estimating all possible information for the cubic model independently. It is unlikely that your data will require such a complex model unless the ranges of the factors are too wide. You may need to reconsider the ranges in order to generate a suitable model for prediction.

Model: Since the model recommended by the Fit Summary often includes insignificant effects or misses important effects we suggest you perform the following regardless of the Process Order proposed by Design Expert…

 

• Choose a Quadratic model for the Process Order
• Use Backward Selection to fit the full quadratic model – all main effects, two factor interaction and quadratic terms have a green M for model
• Click the ANOVA button to automatically and sequentially omit terms with the highest to lowest p-values greater than the Alpha Out threshold 0.1
• If you are asked: Would you like the hierarchy corrected automatically? choose Yes. This ensures that you preserve the hierarchy of your model (i.e., main effects of the factors involved in a significant interaction or quadratic effect will also be included in the model for a suitable testing of its effects)
  

Analysing your Results (ANOVA)

 

Adj R-Squared and Pred R-Squared measure the fraction of variation that can be explained and predicted by your model. Together with the other summary statistics, they provide a numerical assessment of model adequacy

 

Warning: close agreement between your replicate observations can artificially lead to evidence of significant lack of fit.

• The insignificant terms (p-value > 0.1) omitted from the model by the backward selection approach are listed first
• Check the ANOVA (Analysis of Variance) table to assess the importance of the model and the individual terms in the model
• Mean Square column refers to the variance or signal associated with each term (e.g., variation in Hardness due to Liquid Volume is 4.00, while residual or noise variation is just a 100th of its size at 0.04)
• F Value, next column, is the signal-to-noise variance ratio (e.g., the signal or effect due to Liquid Volume is 100 times that due to the noise)
• P-value, final column, is the probability of observing a signal-to-noise ratio as large as in the previous column purely by chance (i.e., the risk of you making the wrong the decision about the importance of the Liquid Volume effect is incredibly small <0.0001)
• The important terms in the model or effects on Hardness appear to be B-Liquid Volume, B2 (curvature due to Liquid Volume) and a smaller CD interaction between C-Inlet Air Temperature and D-Spray Rate
• There are also tests for evidence of Lack of Fit the ratio of variance due to effects not previously selected to include in your model with the Pure Error. If you fail to include large effects then this will inflate the Lack of Fit. Use effect and diagnostic plots (e.g.,  residuals (ei) vs. Factor) to identify potential effects to include to improve your model)

Annotated ANOVA – by default the above ANOVA results come with comments designed to help you interpret the output. If the annotations do not appear, select Annotated ANOVA on the View menu. Help to interpret any value on the output can be gained by highlighting the value and either pressing the F1 key or right clicking and selecting Help 

 

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