# Weighing Scale Calibration

#### Calibrationian

##### Starting to get Involved
Hi all,

A simple question for weighing scale calibration.
We have a standard weights set used to calibrate digital weighing scales.

Just confused with the previous calibration report, in which the used weights as "Nominal Value" was the actual value of the weights from the calibration certificate.
Now here is the scenario:
A certain standard mass weighs 1.00023 grams from the calibration certificate.
After the "Self calibration" of the weighing scale, it measures the standard mass as exactly 1.0000 grams...
Which prompts it to a correction of about -00023 grams...

Should we still put the standard mass of 1.00023 grams for Nominal Value? or simply follow the engravings on the mass that says "1g"?

Thanks...

#### ChrisM

##### Quite Involved in Discussions
What are the uncertainties of measurement on the calibration certificate for the weight of 1.00023g and what are your accuracy requirements for your scales?

#### Semoi

##### Involved In Discussions
If you use the calibrated value 1.00023g, it's nearly impossible to make an error in your argumentation. Thus, you should always stick to the calibrated value.

If the accuracy of the weight is not good enough for your purpose, then you should get a more accurate calibration value. However, even in this case the point estimator 1.00023g is still considered to be the best estimate of the true value.

#### Jim Wynne

Hi all,

A simple question for weighing scale calibration.
We have a standard weights set used to calibrate digital weighing scales.

Just confused with the previous calibration report, in which the used weights as "Nominal Value" was the actual value of the weights from the calibration certificate.
Now here is the scenario:
A certain standard mass weighs 1.00023 grams from the calibration certificate.
After the "Self calibration" of the weighing scale, it measures the standard mass as exactly 1.0000 grams...
Which prompts it to a correction of about -00023 grams...

Should we still put the standard mass of 1.00023 grams for Nominal Value? or simply follow the engravings on the mass that says "1g"?

Thanks...
The question is, I think, how concerned are you about going out to five decimal places in your measurements?

#### Jim Wynne

... in this case the point estimator 1.00023g is still considered to be the best estimate of the true value.
For practical purposes, there is no "true" value. All measurements are subject to uncertainty. As I said in a previous post, what matters is the degree of precision needed. I doubt that it's five decimal places.

#### Semoi

##### Involved In Discussions
@Jim Wynne: I agree with you that the needed degree of precision is important. However, as you are probably aware, the statement in my previous post is not that 1.00023g is the true value, but that this is the best estimate of the true value.

I feel like we are deviating from the main topic, however, if you write
For practical purposes, there is no "true" value.
I wonder what you mean by "practical purpose". In measurement theory the true value is a theoretical value, which we will never know -- unless we use it to define the SI unit. Thus, I would agree to the statement "The calibration weight has an unknown true value".

Jim, I am just poking you. Have a great Sunday.

#### Tidge

Trusted Information Resource
I wonder what you mean by "practical purpose". In measurement theory the true value is a theoretical value, which we will never know -- unless we use it to define the SI unit. Thus, I would agree to the statement "The calibration weight has an unknown true value".

Jim, I am just poking you. Have a great Sunday.
Here is a poke back: True values are only theoretical according to Frequentist statistical theory. Bayesian theory has a different foundation: true values do exist, its just that there exists a degree-of-belief around the true value. Happy Sunday!

#### Semoi

##### Involved In Discussions
@Tidge: I do not really understand your statement. First you say "True values are only theoretical according to Frequentist statistical theory." then you say that "true values do exist [...]". What exactly to you challenge in my statement?

I strongly doubt that my statement "In measurement theory the true value is a theoretical value, which we will never know" is wrong in the Bayesian context. The two perspectives (frequentist and bayesian) differ in their interpretation of uncertainty. Thus, I challenge you to find a paper in which Andrew Gelman (or any other big fish in Bayesian statistics) either states that
(i) a true value does not exists, or
(ii) a true value is not theoretical, but can be known with absolute certainty
in the context of Bayesian theory. One more condition: It's not enough to find a reference where he talks about a possibility that the true value is time dependent. Looking forward to your reply

#### Jim Wynne

This has now gone well beyond the topic at hand. All we need to know is whether the five decimal places have any practical value.

#### Tidge

Trusted Information Resource
I do not really understand your statement. First you say "True values are only theoretical according to Frequentist statistical theory." then you say that "true values do exist [...]". What exactly to you challenge in my statement?
There is no challenge! Briefly The foundation of Frequentist statistics hinges on the concepts of there being a hypothetical ensemble of possible measurements of something; Bayesian analysis (more-or-less) starts with a prior belief in what the actual value of the something is.

In other words: Frequentists (more-or-less, from the first principles of frequentist analysis) believe "if you repeat a measurement an infinite number of times, that's the answer you get for the measurement of the value"...so it isn't the value that is real it is the measurement of the value. Bayesian's will (more-or-less) start with "I believe the value is some range of allowable values (the prior degree-of-belief); do the measurement and we can answer with a calculated degree-of-belief what the actual value is (for the prior belief)." There is a famous (apocryphal?) story about Laplace's wager about the mass of planets (he used a 'Bayesian' methodology). The planets must have mass, independent of any measurements.

The point about Andrew Gellman is odd... I don't think I wrote precisely what you think I did... I certainly don't think he would have written (what was attributed to me?) about Bayesian analysis. We could just ask him if he ever wrote such a thing, but that seems pointless. I would be slightly embarrassed to have AG critique my (over-)simplification of the Bayesian method... the guy has generated a lot of his professional output on the many subtleties of choices-of-priors! I'm a pure dilettante compared to him, as I've almost always stuck to a simple scale-invariant prior and if wanted to make sure I wasn't too crazy with that choice I'd do the same analysis using a flat prior (to make sure results were not radically different).