# Correlation Coefficient and Industry Standards - Corrrelation between two of my CMMs

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Hi all, I just calculated the corrrelation between two of my cmms. my Pearson product moment correlation coefficient value is 0.727. My p value is 0.000. I have rejected the null hypotheses (CL = 95%). With regards to the coefficient (0.727) which indicates the strength of the correlation, are there any industrial standarda or AIAG standards? Is there something like we have in AIAG for GR&R 0 - 10% error - Gage system O.K.; 10% to 30% May be acceptable...?

#### Stijloor

Staff member
Super Moderator
Re: Correlation Coefficient and Industry Standards - Corrrelation between two of my C

A Quick Bump!

Can someone help Brad with his question?

Thank you!

Stijloor.

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
Re: Correlation Coefficient and Industry Standards - Corrrelation between two of my C

The pearson statistic isn't appropriate for assessing measurement systems.
The pearson statistic is for the correlation of a dependent variable with an independent variable. Measurement systems (whether assessign within system repeatability or between system reproducibility/bias) have two independent variables. The first measurement is not dependent on the replicated measurement; One system is not dependent on the other. Additionally, this type of correlation ignores bias. A very critical element of assessments between systems.

If two systems are equal, there will be a 1:1 correlation. If there is error it will appear as variation scattered perpindicular to a 45 degree line. If there is bias the scatter of variation will not be centered on the 45 degree line.

The approach that should be taken is to calculate the Intra Class Correlation Coefficient. The data are plotted on a Youden plot with a square representing the specification.

There is no 'industry standard' for the amount of variation vs the specification. This one of those cases where we are better off plotting the data adn looking at it to assess its usability.

The formulas are in the attached file. I have also attached a spreadsheet that will do the math and graph for you....

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