Accuracy of the Difference

In summary, the scale has an error of e which is treated the same as the error in the sum of two values.
  • #1
liquidFuzz
97
3
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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  • #2
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.
 
  • #3
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.
 
  • #4
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.
 
  • #5
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. 😇
 

What is "Accuracy of the Difference"?

"Accuracy of the Difference" refers to the level of precision and correctness in the calculation of the difference between two values or measurements.

Why is "Accuracy of the Difference" important in scientific research?

Accurate differences are crucial in scientific research as they help to determine the significance and validity of experimental results. They also allow for proper comparisons and conclusions to be drawn.

How is "Accuracy of the Difference" calculated?

The accuracy of the difference is determined by calculating the difference between the two values and then comparing it to the accepted or known value. The closer the calculated difference is to the accepted value, the more accurate it is.

What factors can affect the "Accuracy of the Difference"?

There are several factors that can impact the accuracy of the difference, such as human error, instrument error, and limitations of the measurement tools or techniques used. It is important to control these factors as much as possible to ensure accurate results.

How can scientists improve the "Accuracy of the Difference" in their research?

To improve the accuracy of the difference, scientists can use more precise measurement tools, repeat experiments multiple times, and carefully control for any potential sources of error. Collaborating with other researchers and peer-reviewing results can also help to improve accuracy.

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