the error of lack of fit and analysis of variance

[#1]

i meet a question when i deal with the problems in Design and analysis of experiment.this is a two-level full factorial design with 4 center points.in my opinion，the error in lack of fit is same to the error in analysis.but i dont get the same result in this report.here are relative data and analysis report：

and here is the solution in this book‘s solution manual

i cant get the same result

[#2]

Open Effects Test

[#3]

the result of effect  test have the same question.because of the difference of pure error between lack of fit and analysis of variance，the F-value is relatively large than standard answer.I have tried to add different terms in my model and still dont work.

is there some problems in the terms chosen stage? 

[#4 · Accepted solution]

The JMP results do typically match the book results with one major change. For all of the testing of the effects and the Whole Model, JMP will use the Total Error (which is pure error AND lack of fit error together). The results from the book seem to be using only the Pure Error for the testing. This means that JMP is using a different denominator from the book on all of the F-tests, which changes all of the significance tests/p-values. So all Sums of Squares seem to match. The Curvature line from the book matches the Lack of Fit line from JMP. 

Which is correct is a matter of opinion. I think most analysts would use the Total Error for the testing. Why? If there is significant lack of fit, then your total error term is likely larger than it should be, leading to fewer significant effects. You should remove the lack of fit to get a better model and "see" more significant terms.

If the lack of fit is NOT significant (like this case), then total error still works well because the lack of fit sum of squares is just some random noise and is not significantly impacting the total error line (hence the conclusion, not significant).

I hope this helps. If I have misunderstood the question, please clarify so that we can help further.

[#5]

thank you so much，i get your point.