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- Test For Curvature In 2 level full factorial with center points

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Oct 13, 2015 8:32 AM
(4416 views)

I am used to using Minitab for analyzing a 2 level factorial with some number of center points. In Minitab there is a test for curvature given (as opposed to a lack of fit test in JMP). Is there anything similar in JMP or should I just use the lack of fit test?

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Hello schuprj,

You have at least a couple of options for checking curvature. First is to plot the residual by predicted values under the red hot spot when you use Fit Model to build your model. Go to Row Diagnostics > Plot residual by predicted. Look at the scatter of the residual points and see if they are random or in some sort of pattern. Another option is to fit a main effects only model and then fit a response surface model. Two things will happen if there is curvature. Your fit model will improve if any of the quadratic terms are important to your model and you will see the curvature in your prediction profiler where the curvature terms are active.

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Kind of a simple way to do a curvature test is to check if the model terms that would correspond to the presence of curvature are significant in the parameter estimates. If second order or quadratic terms aren't important you can't really have curvature.

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Hello schuprj,

You have at least a couple of options for checking curvature. First is to plot the residual by predicted values under the red hot spot when you use Fit Model to build your model. Go to Row Diagnostics > Plot residual by predicted. Look at the scatter of the residual points and see if they are random or in some sort of pattern. Another option is to fit a main effects only model and then fit a response surface model. Two things will happen if there is curvature. Your fit model will improve if any of the quadratic terms are important to your model and you will see the curvature in your prediction profiler where the curvature terms are active.

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Thanks for your quick post. As followup or clarification, a fairly

standard and simple test for curvature in this situation is to compare the

average of the center points to the average of the corner points. If this

difference is big enough then you probably have curvature and this warrants

further study to identify which factor(s). I can do this test manually in

JMP but thought that a fairly standard test like this would be displayable

somewhere in the dialogue. If not, so be it.

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Hi schurpj,

Regarding to your lack of fit comment. Lack of fit - if significant - shows you there is something missing in the model which would improve the model significantly. This does not necessarily have to be a quadratic effect. it also could be a missing interaction effect or something you didn't measure but will have effect on your response.

"The difference between the error sum of squares from the model and the pure error sum of squares is called the lack of fit sum of squares. The lack of fit variation can be significantly greater than pure error variation if the model is not adequate. For example, you might have the wrong functional form for a predictor, or you might not have enough, or the correct, interaction effects in your model." (documentation)