Chi Square Analysis

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• #33985

Anonymous
Participant

The scenario is as follows:
A group of identical machines are used to process a piece of material into a pressed form, which is then conveyed to the next process.  Independently, these machines all tend to jam occasionally but overall they operate at desired efficiency.
A new material is now being used, with a slightly different material shape.  The question for my organization is whether or not jams are occurring more frequently with the new material.
Data was collected with the old material and with the new material.  It can be said for individual machines that some do have a statistically different jam occurrence with the new material and some do not have any significant difference.
I decided to use Chi Square a little further (continuous data will be evaluated in time).  For now, count data is all that will be available.  The modified method is as follows:
Pairwise comparisons of each machine with all other machines was made, first with the data from the old material.  Then, pairwise comparisons were made between all machines using only new material.  Finally, pairwise comparisons were made between different machines using only “old vs. new” material in each comparison.
The object was to determine if the number of significant difference between machines was different depending on whether the comparison was “new to new”, “old to old” or “new to old”.
The chi square analysis indicates that differences in the number of “significant differences” is not significant (machine differences with old material = machine difference with new material = machine differences with old vs new material.
I am wondering if anyone has used chi square in such a manner and if anyone has any thoughts on the matter.

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#93045

anon
Participant

So you are saying that you are evaluating the whether “independence” is independent of the type of pairwise comparison?  (Pairwise between old material and old material, pairwise between old material and new material, and pairwise between old material and new material).
If the new material makes a significant difference, then the pairwise comparisons between old material and new material should show more rejections of the null hypothesis than the others.
Interesting concept.  Let me think it through and post later.

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#93100

Anonymous
Participant

Does anyone have any comments on this use of Chi Square?Your thoughts would be appreciated.

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#93106

Mikel
Member

Just remember Dr. Mikel calls it the Shopsmith of statistical tools.

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#93200

AbetF
Participant

Anonymous,
You will surely get this result :
======= The chi square analysis indicates that differences in the number of “significant differences” is not significant (machine differences with old material = machine difference with new material = machine differences with old vs new material.========
On your first order chi square test, it shows that your material factor ( old and new ) is not dependent on your machine factor ( mach1, mach2…etc.) but your machine factor is dependent on your material factor ( at least one machine is dependent on materials used ) that’s why there are some that has significant difference.
When you use second order chi square ” I like to call it second order ,” the factors used are materials ( three combinations; new-new, old-old, and old-new) and difference( significant and not significant ). this would surely result to a no significant difference because the material factor and difference factor are independent to each other. the Machine factor was not anymore included on the analysis which is the one dependent to the material factor.
If you say that there is no difference between the two materials, you will be correct with your conclusion, but the machine to machine variation is significant. maybe even when you were still using the old materials ( if there’s at least one significant difference on the machine with old to old pair).
Hope this helps,
AbetF

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#93586

Anonymous
Participant

Thanks your your input. I believe I understand your comments. The hypothesis being tested would be stated as follows:Ho: Significant differences between pairwise comparisons of machines are independent of materialHa: Significant differences between pairwise comparisons depend upon material.As such, the indication is that there is no evidence to say that there is a significant difference based upon material type.Is that correct?

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#93593

AbetF
Participant

Actually, it’s good to experiment with the tools but we need to understand the foundation or the basics of that particular tool. what we do here is we try to compute each tool manually and if possible try to derive the formulae. In this case, first order chi square is enough to prove what you want to test. If you do the second order chi square test, It may lead you to a wrong conclusion.
I would like to make some corrections on the statement I made on my first posting:
“On your first order chi square test, it shows that your material factor ( old and new ) is not dependent on your machine factor ( mach1, mach2…etc.) but your machine factor is dependent on your material factor ( at least one machine is dependent on materials used ) that’s why there are some that has significant difference.”
It should be “the material factor is dependent on the machine factor and the machine factor is independent to the material factor.”

Abetf

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