Why can't I detect curvature (nonlinearity) in DOE in JMP?

[#1]

In Minitab, if the factors in the DOE have center points, the curvature will be directly tested (i.e. nonlinearity, p<0.05 indicates that the curvature is significant), but there seems to be no such function in JMP?

[#2 · Accepted solution]

Hi @Xinghua,

The test for curvature in DoE is a frequent topic in the Community and has already some solutions. Please refer to the following posts and add-in :

Test For Curvature In 2 level full factorial with center points 

Another post on how to test for curvature in two-level factorial with center points, including discu... 

How to do a test for curvature in a DOE with JMP 

Pure Quadratic Curvature Test Add-In 

I think these references will help you,

[#3 · Accepted solution]

Many options in JMP to test for curvature with a DOE:

1. Choose a response surface design from the DOE > Classical menu.

2. Choose a Custom design and include quadratic (or higher) power effects.

3. Choose a Definitive Screening Design and include center points to estimate quadratic effects.

[#4]

Hi @Xinghua : Seems to me, the easiest thing to do would be to include the quadratic effect of any one of the factors in the model. The p-value for that effect is then the p-value for testing curvature.  Be warned though, whichever factor you used here may or may not be the factor that the quadratic effect is assigned to (it is confounded with the other potential quadratic effects). It's just a test to see if there is curvature present in at least one of the factors, so you will still need to augment the design to tease out which facture(s) is quadratic.

[#5]

Thank you very much. I tried it, but for some reason, the p-value of the factor square is not numerical. I don't know why.
I uploaded the data, you can analyze it. Thanks.

[#6]

Hi @Xinghua,

Since you only have centre points, you can only check curvature and estimate one quadratic effect (out of the 4 possible ones). If you add all 4 quadratic effects in the model, JMP will inform you there is a singularity in the model, as it won't be able to estimate independantly all 4 quadratic effects only with centre points :

To estimate all 4 quadratic effects, you need to have different points available, middle level factors (with 0 for the factor you want to estimate the quadratic effect, and +/-1 for other factor levels), instead of centre points (with 0 for all factors levels).

Try re-fitting your model only with one quadratic effect, and you will be able to estimate p-value for this quadratic effect, and lack-of-fit test :

The p-value of this quadratic effect clearly shows a curvature in your response (as well as the plots you have shown in your latest response). The p-value for this effect is calculated with the null hypothesis being "this effect is not significantly different from 0". So as the p-value is very low here, you can be quite confident that this effect seems to be statistically significant from 0, and that a curvature/quadratic effect is clearly visible. Adding a quadratic effect in you model enable to have a more adequate model (lack-of-fit test doesn't show very low p-value, so the model seems more adequate).

If you fit a model only with main effects and 2-factors interactions, you already had some hints that something more was probably hidden, as the lack-of-fit test shows a very low value (so the model may not be adequate) and actual vs. predicted and residual plots seem to indicate a curvature :

Please see the article How to do a test for curvature in a DOE with JMP I mentioned before if you want to test curvature with a similar output as in Minitab :

Hope this answer will help you, 

[#7]

Thank you very much for your enthusiasm.
I can confirm that in a DOE factorial design, if he center points are used, then there will only be combinations of the center points of the factors (if there are 4 factors, then there will only be 0000, not 000+, +-0 +...), if RSM is used, there will be a combination of the center point of one factor and any level of other factors (if there are 4 factors, there will be 000+, +-0+, 0000...).

[#8]

While I haven't looked at the links provided by @Victor_G , and I agree with everything others have contributed to date, my first step, always, never fail, before any statistical test p, t, F, or otherwise, is to plot response vs. factor scatter plots. I hope at least one of those references encourages this approach. Your eye and process knowledge are the most sensitive 'detectors' of effects I've ever encountered. In 30 years of practice of DOE in an industrial setting I honestly can't recall one experiment we analyzed where a LOF test for curvature was 'significant' that didn't show up in scatter plots first.

[#9]

Thank you very much.

DOE can generate leverage graphs, even with p-values. But I'm not sure what that p-value (if less than 0.05) means.

[#10]

The leverage plots are a graphical way to test the hypothesis that the slope of the coefficient of for a given factor = 0. It can also be used for other purposes. See the JMP documentation for a thorough explanation.

Leverage plots in JMP The p value is interpreted as any other p value for a parameter estimate. Only amplitude is below the 0.05 threshold...if that's a threshold you want to use.