# DoE and ANOVA - 4 factor and 3 levels Taguchi design with 2 replicates

C

#### cristiano74

Dear listers,
I've a dataset from a 4 factor and 3 levels Taguchi design with 2 replicates.

I'd like to perform an ANOVA to find the interaction between factor.

Could I use ANOVA procedure as it is, or I should follow some other ways?

Any kind of help would be greatly appreciated,thanks

Cristiano.

#### Statistical Steven

##### Statistician
Staff member
Super Moderator
Re: DoE and ANOVA

You did not make it clear if you are running an L9 or L27 array. Regardless, Taguchi designs are not intended to estimate interactions. You can probably graph the interactions to see if there is anything visually, but your selection of a Resolution III design prohibits the estimation of interactions.

C

#### cristiano74

Re: DoE and ANOVA

It' s a L9 with 2 preplications, as you can see in the table below, I suppose.

Now I should display via ANOVA the interacions: my teacher send me this table for homework.

runs A' B' C' D' outcome
1 -1 -1 -1 -1 1075
2 -1 0 0 0 633
3 -1 1 1 1 406
4 0 -1 0 1 860
5 0 0 1 -1 561
6 0 1 -1 0 868
7 1 -1 1 0 669
8 1 0 -1 1 1138
9 1 1 0 -1 749
1' -1 -1 -1 -1 1052
1'' -1 -1 -1 -1 1037

What could I use to solve this problem?

thansk agin for your collaboration.

C.

#### MasterBB

##### Involved In Discussions
Re: DoE and ANOVA

Cristiano,

Statistical Steven is correct and agree (referring to interaction).
What is the objective of the Response? Is it to hit a Target, Minimize or Maximize.

You can certainly graph the factors & it's interaction (See SS response). Don't recommend.

I am not quite sure why is your teacher is asking for an interaction plot when given a Taguchi array.

See attached (hope this helps)

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#### Miner

##### Forum Moderator
Staff member
Re: DoE and ANOVA

Regardless, Taguchi designs are not intended to estimate interactions. You can probably graph the interactions to see if there is anything visually, but your selection of a Resolution III design prohibits the estimation of interactions.
This is not quite accurate. In this specific case, you are correct since all four columns were fully utilized with factors. However, Taguchi designs can be used to evaluate specific interactions if they are suspected in advance and planned as part of the design. This interaction must be assigned to the correct column, which then cannot be used for a factor.

Taguchi designs are normally used as screening designs. Confounded relationships can be further explored with higher resolution designs after the numerous non-significant factors have been eliminated.

C

#### cristiano74

Thanks to all, and I dont make my homework because my teacher uses a design to understand the interactions with ANOVA when in fact he does not know what to do?

It often happens when engineers draw the statistics

How can I explain to him that ANOVA is not the best technique in this case?

Thanks again.

C.

A

#### Allattar

Correction.
Taguchi is not the best approach for analysing interactions.
ANOVA is the right approach to the analysis.

Taguchi designs really need to rely on an outer array of noise variables as well, which I cannot see that you have used. Seeing as stability to noise or the environment is what Taguchi is all about, by not testing at two environment levels (ie two columns of response) sort of goes against what you would be using a taguchi design for.

You would be better off with a standard factorial design here, with 2 levels per factor I think. Unless you have a specific reason why you need 3 levels per factor.
If you are fitting only linearity and you have numeric inputs you do not need 3 levels on each factor. You can use a centre points instead to check for curvature.

If you have categorical factors with 3 fixed settings then the 3 level factorial designs can be useful.
There is no point creating a factorial design with 3 levels per factor if your only going for a linear fit on numeric inputs. The standard 2 level factorials give you the simplest and least runs for a design.

If you absolutely have to have more than 2 levels on a factor you can use the choice to select optimal design to tell it which interactions you need and get it to reduce the design from there.

I probably haven't explained this enough, but I am worried that you are diving into Taguchi designs without an appreciation of how you are supposed to use them, and trying to use them for something they are not very good at, eg: finding interactions.

My advice on doe is start with the factorial designs as a base of understanding, then move to look at why and where you might use the others.

I get worried by the buzzword that is Taguchi.

#### Statistical Steven

##### Statistician
Staff member
Super Moderator
Re: DoE and ANOVA

This is not quite accurate. In this specific case, you are correct since all four columns were fully utilized with factors. However, Taguchi designs can be used to evaluate specific interactions if they are suspected in advance and planned as part of the design. This interaction must be assigned to the correct column, which then cannot be used for a factor.

Taguchi designs are normally used as screening designs. Confounded relationships can be further explored with higher resolution designs after the numerous non-significant factors have been eliminated.
Miner -

I believe if you use a column of your Taguchi array for the interaction it would have to be the correct column where the interaction is confounded. Typically when this occurs you are not reducing the run total enough to justify its use. For example, assuming the OP was interested in only one ogf the interactions therefore reduced it to a three factor, 3 level design. This is just a 1/3 fractional factorial, so no need to use the Tachugi array per se.

Though, I agree it can be done, I have never seen it applied successfully.

#### Statistical Steven

##### Statistician
Staff member
Super Moderator
Correction.
Taguchi is not the best approach for analysing interactions.
ANOVA is the right approach to the analysis.

You would be better off with a standard factorial design here, with 2 levels per factor I think. Unless you have a specific reason why you need 3 levels per factor.
If you are fitting only linearity and you have numeric inputs you do not need 3 levels on each factor. You can use a centre points instead to check for curvature.
Just to add to your excellent response, if you have a four factor, two level study, the full factorial would be 16 runs. A 1/2 fraction would 8 runs. So you can run a single run at the center point.

#### Miner

##### Forum Moderator
Staff member
Re: DoE and ANOVA

Miner -

I believe if you use a column of your Taguchi array for the interaction it would have to be the correct column where the interaction is confounded. Typically when this occurs you are not reducing the run total enough to justify its use. For example, assuming the OP was interested in only one ogf the interactions therefore reduced it to a three factor, 3 level design. This is just a 1/3 fractional factorial, so no need to use the Tachugi array per se.

Though, I agree it can be done, I have never seen it applied successfully.
You are correct about reserving the column where the confounding occurs. I did not claim that it was efficient, but in my earlier days when Taguchi was new, I have successfully used the approach many times. Now I have learned to do the same things in a more efficient manner.

For example, Box has shown how the inner and outer array approach can be done more efficiently using a Split-plot design. We learn new things. It does not make the old way wrong, just less efficient.

Before computers made the calculations easy, Taguchi's approach was great, because the math was easy. I date back to those days. I had to perform the calculations by hand for years before getting one of the first IBM PCs (pre-XT). That was his intent.

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