Statistical test for the lack of fit

The value of F calculated in this manner can be tested against a tabular critical value of at a given level of confidence (see Section 6.5), or the level of confidence at which the calculated value of is critical may be determined (see Section 6.6). 

If the null hypothesis of Equation 9.44 is disproved (or is seriously questioned), the conclusion is that there is still a significant amount of the variation in the measured responses that is not explained by the model. That is, there is a significant lack of fit between the model and the data. 

We emphasize that if the lack of fit of a model is to be tested, f-p (the degrees of freedom associated with 55, f) and n - p (the degrees of freedom associated with 55pj) must each be greater than zero that is, the number of factor combinations must be greater than the number of parameters in the model, and there should be replication to provide an estimate of the variance due to purely experimental uncertainty. 

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