# Correlation Analysis with Delta

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- This topic has 5 replies, 4 voices, and was last updated 6 months, 3 weeks ago by Chris Seider.

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- February 21, 2020 at 7:13 am #246269
Hi, I’m studying a correction between two sets of test data. There is a correlation between the two sets of data with coefficient more than 0.6. However, there is fixed delta between the two sets of data and there are low and high limits applies to the test data.

May i know how do i justify if the delta is significant against my test limits?

- This topic was modified 7 months ago by Yeoh.

0February 21, 2020 at 1:18 pm #246279

Robert ButlerParticipant@rbutler**Include @rbutler in your post and this person will**

be notified via email.I think you will have to provide more information before anyone can offer much in the way of suggestions. My understanding is you have two populations which have a specified (fixed) difference between them and you want to know if this fixed difference is less than or greater than the difference between the lowest and highest spec limits associated with the two populations. If this is the case then all you have is an absolute comparison between two fixed numerical differences. Under these circumstances there’s nothing to test – either the fixed delta is greater or less than the fixed delta between greatest and least spec and things like correlation have nothing to do with it.

0February 22, 2020 at 10:13 pm #246316Apologized for didn’t provide additional information.

Generally, i have two sets of data namely A and B which are collected using two different hardware platform, namely A and B. I collected the data by using 30 samples with both platform A (old) and B (new) and check if the two platforms are correlated. If they are correlated, then i will replace the old platform with the new platform. Additionally, each of these sample has to be within 9.80 and 13.80 for both platforms. For sake of simplicity, i just show 5 samples data in my snapshot below and these samples are one-to-one comparison.

Based on the analysis, the correlation is good with Rsq > 0.8. However, there is fixed delta about 0.25 between Set A and Set B and i want know if the delta of 0.25 is critical against the limits of 9.80 – 13.80. If the delta is significant enough, which means i cannot replace the platform A with new platform which is B.

I have attached some sample data as snapshot. Please advise.

0February 24, 2020 at 11:13 am #246340

Fausto GalettoParticipant@fausto.galetto**Include @fausto.galetto in your post and this person will**

be notified via email.February 24, 2020 at 1:41 pm #246342

Robert ButlerParticipant@rbutler**Include @rbutler in your post and this person will**

be notified via email.The problem you are describing has two parts. The first part isn’t one of correlation rather it is one of agreement. Things can be highly correlated but not be in agreement. I would recommend you use the Bland-Altman approach to address the agreement part of the problem.

Bland-Altman

1. On a point by point basis take the differences between the two methods.

2. You would like to be able to compare these differences to a true value but since that is rarely available use the grand mean of the differences. Compute the standard deviation of the grand mean of the differences and identify the +- 1,2, and 3 standard deviations

3. Next compute the averages of the two measures that were used for computing each difference.

4. Plot the differences (Y) against their respective average values (X).

5. If you have a computer package that will allow you to run a kernel smoother on this data and draw the fitted line do so. If you don’t then you can use a simple linear regression and regress Y against X and look at the significance of the slope. If you can only do the simple linear fit you will want to plot that line on the graph. The main reason for doing this is to make sure the significance (or lack thereof) isn’t due to a few extreme points.

To determine agreement you will want to see if the mean of the differences is close to zero. If there is an offset, but no trending then you will have identified a bias in the measures (based on the example you have provided this is to be expected). If you have a significant trending and it is not being driven by a few data points then you will have a situation where the two methods are not in agreement. If they are not in agreement then you have some major issues to address.

The second part is the issue of the approximate delta of .25 relative to the lower (9.8) and upper (13.8) limits.

It looks like you have the following possibilities:

1. The difference is approximately .25 and both processes are inside the 9.8-13.8 range

2. The difference is approximately .25 and one process is outside either the upper or lower target and the other process isn’t.

3. The difference is approximately .25 and both processes are outside of either the upper or lower targets.

Your post gives the impression that a single instance of the approximate delta of .25 being associated with either of the processes outside the targets counts as a fail. If this is true then the question becomes one of asking what are the probabilities of getting a difference of approximately .25 given that one or both of the processes are outside the target range and building a decision tree based on what you find.

0February 24, 2020 at 7:26 pm #246353

Chris SeiderParticipant@cseider**Include @cseider in your post and this person will**

be notified via email.I think you’ve forgotten an important thing. Do a gage R&R for both devices before going first.

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