Anova question…
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 This topic has 4 replies, 2 voices, and was last updated 14 years, 6 months ago by annon.

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January 29, 2008 at 3:24 pm #49220
When the ANO VA method is used for assessing a DOE effort, what is the practical and technical explanation for the ‘lack of fit’ term? What is it referring to in terms of significance? Thanks!!
0February 7, 2008 at 1:49 pm #168305Annon,
Lack of fit is the difference between the approximation model and the truth. Basically it describes the bias that you have between your model and the true data. You can include special runs in your DOE (eg center points) to help describe the fit. If your DOE maximizes the design efficiency then there will be no lack of fit.
The lack of fit follows the same type of null hypothesis test where you would presume that the data fit the model until proven otherwise. You would follow the type I error to determine the significance of the lack of fit (eg alpha = 0.05). Lack of fit tests can run on the conservative side so you may need more data to make a decision.0February 7, 2008 at 4:49 pm #168315Jen,
Thanks! So if I understand, this lack of fit entry in the ANOVA is simply determining if the predictive model can adequately approximate the true value for the predictive Y and uses a null of ‘good fit’.
I would assume this ANOVA entry is used in conjunction with the residual analysis (in particular the residual v. fitted value plot) to determine how the model is lacking (assuming pvalue < alpha). For example, requiring additial 1st order terms, 2nd order or quadratric terms, transformation, etc.
Is that a correct statement?0February 7, 2008 at 5:44 pm #168319Annon,
Yes. Basically if your lack of fit shows as significant you would want to introduce more data. You could add additional trials to your original design. These trials may be centerpoints or going through Response Surface Methodology where you would begin looking at more of a surface as the model you are trying to fit.
0February 7, 2008 at 9:49 pm #168331Jen,
I am tracking now, thanks.0 
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