Reporting results query

Hello, I've recently started work for a small company that has an in-house calibration facility for testing mass standards using Borda's substitution method. We are not accredited to 17025 but are working towards it and I'm learning on the job, so to speak.

We hired a consultant who said that the results we report have 1 too many decimal places. The example he pointed out is a certificate for a 1 kg weight, calibrated on a 4 decimal place comparator. The results reported was 1 000.001 36. His argument is that as the comparator only has 4 decimal places, we can only report to 4 decimal places. He said the result should be 10 000.001 4, but I have a couple of problems with this.

First, if he is correct about only using the readability of the comparator, then I'd argue that the 4th digit should not be rounded, as according to him, there is no 5th digit that exists to round it.

Second, we are not using the comparator to weigh the standard, but we are using it to compare the standard to another (higher accuracy) standard (which has a reported result to 5 decimal places). As we are using Borda's method, surely the reported result is a calculation of averages and not a reading taken? To me it's like saying the average of 3+3+3 is 4 or 5, not 4.5.

I'd be appreciative of anyone else's thoughts on the matter. I'm happy to be wrong, but I'd like to understand why. Thanks in advance.

 

Good day @Smithy87 ;
Welcome to the site.

Please help us understand. If the comparator only goes out (displays) to four decimal places, then where does the fifth decimal reading come from? (i.e., In your example, where does the "6" come from ?)

Thanks in advance for helping us understand.

Be well.

 

Hi John, Thanks for responding to me and my apologies for the delay in responding. The figure comes from the average of the individual readings.

As a simplified example, using Bordas method, 5 readings are obtained (Ai being the standard weight, Bi the weight under test):

A1 2.0002
B1 2.0007
A2 2.0008
B2 2.0008
A3 2.0008

The average of the A readings is 2.0006. The average of the B readings gives 2.00075. Deducting A from B gives us the difference between the standard and the weight under test, this being -0.00015 in the example. Here, 5 is the 5th digit and it has been practice, I believe to leave it.

It's been practice in the department to report to one more decimal place than the comparator on the basis that the result provided is not a direct reading, but an average of the differences. I'll come clean and admit I am new to all this (I used to work in the admin dept but due to staff departures I've been drafted in to help due to my experience in project management) however, statistics and maths isn't my strongpoint. My viewpoint is based on current practices in the laboratory. I am being told one thing by the consultant and another by the person who's worked here longest (and has worked in the past for accredited laboratories) - I might just get a new job

I hope that explains matters but please let me know if I can clarify anything. Thanks

 

Thanks for clarifying @Smithy87 . Did your consultant mention the basis for his/her comment "...too many decimal.."? "Too many...." based on what?

I would respectfully disagree with his/her claim.

HOWEVER, I would mention that you may be opening yourself up for complaint/criticism by your "customer" . i.e. What is the "need" to over-commit" to an implied level of accuracy beyond your equipment reading? What is the specification/claim (in regards to degree of accuracy) for the standards you are testing?

For example, when I was involved with a 17025 laboratory conducting product verification for customers, if the equipment measured to four decimal places, but the part drawing only went to three decimal places, we ONLY recorded data out to three decimal places, for obvious reasons.

Hope this helps.

Be well.