Gage R&R Anova - With Interaction or without Interaction?

Rameshwar25

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#1
1. When to use 'without interaction' and when to use 'with interaction' study in GRR-Anova?

2. What is difference in Nested and crossed methods? Are formulas different in both cases?
 
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Miner

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#2
Re: Anova- With interaction or without interaction?

1. When to use 'without interaction' and when to use 'with interaction' study in GRR-Anova?

2. What is difference in Nested and crossed methods? Are formulas different in both cases?
  1. Go by the p - value for the interaction. If the p - value is less than or equal to your previously established alpha level (e.g., 0.05), then use the interaction. If greater than alpha, do not use the interaction. See my blog for additional information and an ANOVA spreadsheet that allows you to pool the non - significant terms.
  2. Nested studies are those where the "parts" cannot be retested. Crossed studies are those where that "parts" are retested. The math is different, so use the correct analysis for the particular study.
 

Rameshwar25

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#3
I have tried to understand it using an excel sheet which I downloaded from elsmar.com. Still i have some queries.
1. as per MSA 4th ed, page 198, the F-value for interaction (0.434) has been compared with F(0.05,18,60) i.e. 0.99999 whreas in the downloaded excel sheet it has been compared with F(0.25,18,60) i.e. 0.513. Which method should I use?

2. There is another column in table A4 marked as 'EMS' on page 198 of manual. What is the use of EMS while taking decision about the measuring system.

3. on page 197, on top, there is a text like " ... compare the F-static to an upper percentage point of an F distribution with numerator and denominator degree of freedom..... Is this another method of comparing P-value with alpha level..

The excel shhet is attached herewith.
Kindly help.

Rameshwar
 

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Miner

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#4
1. as per MSA 4th ed, page 198, the F-value for interaction (0.434) has been compared with F(0.05,18,60) i.e. 0.99999 whreas in the downloaded excel sheet it has been compared with F(0.25,18,60) i.e. 0.513. Which method should I use?

2. There is another column in table A4 marked as 'EMS' on page 198 of manual. What is the use of EMS while taking decision about the measuring system.

3. on page 197, on top, there is a text like " ... compare the F-static to an upper percentage point of an F distribution with numerator and denominator degree of freedom..... Is this another method of comparing P-value with alpha level..
  1. Note that the spreadsheet was created to allow you to enter your desired alpha value into cell F4. You can use 0.25 if you so desire. The alpha value is you level of risk tolerance that you may be wrong. For example the 0.25 used by AIAG allows a 25% chance that you will accept the interaction as significant when, in fact, it is not significant. An alpha of 0.05 reduces this risk to 5%.
  2. I will check this later when I have access to the manual.
  3. This explains how to obtain the p - value from a table of the F - distribution. The spreadsheet does the same thing using the FDIST command.
 

Miner

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#5
2. There is another column in table A4 marked as 'EMS' on page 198 of manual. What is the use of EMS while taking decision about the measuring system.
EMS is the Expected Mean Squares. When evaluating a RANDOM model, you must use the General Linear Model (GLM) instead of ANOVA. The error terms for a RANDOM model are different from the error terms of a FIXED model. The EMS column simply shows how these terms are calculated. You do not used them directly to make decisions.
 
K

keithljelp

#6
Hi,

When using the ANOVA method for a GR&R the only difference between a fixed effects model and a random effects model is that in the random effects model F values for parts and operators are calculated by dividing the mean square for parts by the means square interaction

Fo=MSa/MSab

and the mean square for operators is divided by the means square interaction.

Fo=MSb/MSab

The F value for operator*part interaction is the means square interaction divided by means square error.

Fo=MSab/MSe

My reference is Montgomery, 6th ed, "Design and Analysis of Experiments", Ch13, p 491

If the interaction of operators*parts is not significant then the GR&R is calculated like a fixed effects model.

I had a brain fade on this point a couple of weeks ago and felt very dumb when I looked at my old Montgomery text.

Keith Jones
 
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