How Is Error Managed When Measuring the Difference Between Two Values?

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Discussion Overview

The discussion revolves around the management of error when measuring the difference between two values, specifically in the context of weighing a small mass using a scale with a specified error. Participants explore how to quantify and treat measurement errors in this scenario.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant describes a scenario involving the measurement of a mass of approximately 5 μg using a scale with an unspecified error e, and asks how to treat this error when calculating the difference between two measurements.
  • Another participant notes that the term for the container's weight is tare and emphasizes the importance of specifying the error e, providing examples of how different values of e affect the ability to measure the 5 μg mass.
  • A later reply introduces the idea that error e can be presented linearly, suggesting that measurements can be expressed as Δm±e rather than Δm±2e or Δm as if the error is constant.
  • One participant asserts that the error in the difference of two values is treated the same as the error in the sum of two values, proposing that the difference can be viewed as adding a negative value with the same error.
  • Another participant agrees with this approach and mentions the use of a "magic formula" with partial differentials to calculate error, although the specifics of this method are not detailed.

Areas of Agreement / Disagreement

Participants express differing views on how to treat measurement errors, particularly regarding the treatment of error in the context of differences versus sums. There is no consensus on a definitive method for managing these errors.

Contextual Notes

Participants have not specified the exact nature of the error e, nor have they resolved how to apply different error models to the measurements discussed. The implications of treating error as linear versus random or constant remain unresolved.

liquidFuzz
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Me and some colleagues discussed accuracy of measurements. We didn't agree on how to treat the accuracy if two values are used to find the value, i.e. the difference between two values.

Situation (explanation)
The weight of a mass m of approximately 5 μg is to be scaled. The scale has an error e. How would you treat the error in this measurement if the scaling is done as such. 1 m is scaled in a ≈2 g container. 2 the ≈2g is scaled without m. 3 the difference is between measurements 1 and 2 is used to find m.

What is the error in this measurement?

Cheers!
 
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First, the term for that ≈2g is tare.
What you have not specified is the error: e.

In general, the accuracy of a scale is specified by a weight.
For example, if e=10μg, then you will not be able to weight your 5μg mass.
If e=1μg, then you should be able to measure your mass to within 1ug. But since two measurements are made it is possible to have a worse-case situation where the error is 2μg.

Sometimes e is specified as a percentage.
So if e = 0.1%, you will not be able to measure 5μg with 2g of tare.
If e = 0.0001%, you will be able to measure 5μg with 2g of tare to within 2μg.
 
Hi, thanks for the input! Sorry if the example wasn't well thought out...

I found some data sheets for the scales. It seems it is accustom to present the error e as linear, thus the measurements for m can be presented as Δm±e, not Δm±2e as if the error is random, or Δm as if the error is constant.
 
liquidFuzz said:
Me and some colleagues discussed accuracy of measurements. We didn't agree on how to treat the accuracy if two values are used to find the value, i.e. the difference between two values.

The error in the difference of two values is treated the same as the error in the sum of two values. Just think of the difference as adding a negative value with the same error.
 
bobob said:
The error in the difference of two values is treated the same as the error in the sum of two values. Just think of the difference as adding a negative value with the same error.

Yes Sir i agree 👍
And then if you need relative error then divide in the end 💪

By the way you can also use the magic formula with partial differentials to get to error. 😇
 

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