# F and P-value in L9 Taguchi Design

J

Dear Friends,

I used a L9 (4 factor in 3 level) design with 2 repetition. But in ANOVA table there are any value for p and F. (only * instead any value). How can I solve this problem.

Thank you

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#### Miner

##### Forum Moderator
You have a fully saturated model. This means that all degrees of freedom have been used by the terms in the model with none remaining for the residual error, which is used to calculate the F ratio and the p-value. In Taguchi designs, any time you assign a factor to all columns, you have a fully saturated design.

You must remove the weakest term from the model to solve this issue. This would be either Time or R. I usually look for the smallest Adj MS and remove that term from the model.

Also, remember that Taguchi OAs are resolution III, so your factors are aliased with 2-way interactions. Minitab does not display this alias structure, so you will have to look at the linear graphs for the L9 OA.

J

dear Miner
I'm not perfect in Minitab. If it possible for you to send your revision minitab file for me.

Thank you.

#### Miner

##### Forum Moderator
This is saved in Minitab 16 format. If you are using an older version, I can save it as a Minitab 15 format also.

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J

Dear Miner

I agree with you. But in attached paper another way to solve F and p Value calculation. Is it right?

Thank alot

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• main.rar
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#### Miner

##### Forum Moderator
Please specify which paper and what page shows the method. I could not find details sufficient to support what appear to be serious flaws in their analysis.

The first paper uses an incorrect number for degrees of freedom and plots interaction graphs which should never be done when using a resolution III design except under special design considerations which were not followed.

The second paper also uses an incorrect number for degrees of freedom.

Neither paper explains where they obtain the variance used in the residual error to calculate F and P.

J

Thanks dear miner

You are right. Neither of paper don't explain how calculate DF, F and P. My question is this, how they obtained this parameters (F, P and DF)?
on the other hand, in my design, all of factors should be exist in ANOVA Table and S/R main effect plot.
In you proposed way, R removed in ANOVATable. So, with your idea, which ANOVA Table I should be report? A ANOVA Table after removing R or before removing of it? a paper similar to your way (paper 3) attached here. Is it correct paper? But in another paper that similar to paper 3, different DF was reported.
moreover in another paper (paper 5) different way (3rd way to calculate F, P, DF) was reported.

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• Paper_3.pdf
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• paper_4.pdf
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• paper_5.pdf
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#### Miner

##### Forum Moderator
Okay. Good news / bad news.

Good News: I figured out what they must have done by dredging up something I learned 30 years ago from Yuin Wu.

When you have three levels, you can calculate a linear effect separate from the quadratic effect. Each analysis uses 1 degree of freedom. The authors apparently calculated and reported the linear effects and pooled the quadratic effects into residual error allowing calculation of F and p. The degrees of freedom would then add up correctly. See below for more information.

Bad News: Minitab cannot do this. You must calculate it by hand or use other software (don't ask which).

Main-effect linear/quadratic estimates. The Effect estimate for linear effects can be interpreted as the difference between the average response at the low and high settings for the respective factors. The estimate for the quadratic (non-linear) effect can be interpreted as the difference between the average response at the center (medium) settings and the combined high and low settings for the respective factors.

Regarding which ANOVA table to report, I would show the reduced model.

J

you are very expert in this regards. But I'm a novice in this area.

Your means is that I calculate F and P with the way that used in paper 1 and 2.
and what's your opinion about paper 5? Is have a correct way?

Thanks again.