Understanding Measurement Uncertainty: Calculating Accuracy and Precision

In summary: Very helpful thank you.You may be able to estimate the error of an instrument if you understand how the instrument works.If you are visually estimating a length against a set of graduations (like a ruler, or a graduated cylinder with liquid), the rule of thumb is that the error is 1/10 of a graduation. If the device is sensitive to electronics noise, you may be able to calculate the thermal noise in an amplifier and noise in a A/D converter.If the device is a photon counting device, then your intensity measurement will have a shot noise component, proportional to sqrt(n). There may be other sources of noise that also...If you are visually estimating a length against a set of graduations (like a
  • #1
fonz
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I have seen similar threads on here but not one with any detailed answer so I felt I would ask myself.

I took a short undergrad module in measurement and uncertainty, intended to prepare for the numerous lab sessions and reports that would follow in the proceeding modules. In that particular module the concept of uncertainty was introduced along with a basic method of calculating the uncertainty from a set of results. Without going into detail the method to calculate the uncertainty essentially relied upon repeated measurements to be taken and the uncertainty derived by some statistical analysis of the results.

What never crossed my mind at the time was the question where does the accuracy (and precision) of the instrument used to record the results factor into this estimate?

Suppose that I were to make just one measurement using an instrument with a specified accuracy then want to find the uncertainty of the measurement I have just made, how is this acheived?

And finally, let's say I have the stated accuracy of the instrument from the manufacturer and the calibration tolerance. What is the relationship between the two and how do they contribute to the uncertainty?
 
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  • #2
In general you can split your uncertainty into two components:
- systematic: you are wrong in the same way no matter how often you repeat the measurement. This can be a ruler that is too long or a poorly calibrated scale or similar things.
- statistical: you are wrong in a random way each measurement. You can often estimate this by taking multiple measurements. If that is not feasible you can use other, experiment-dependent approaches to estimate this uncertainty.
fonz said:
And finally, let's say I have the stated accuracy of the instrument from the manufacturer and the calibration tolerance.
If in doubt, ask the manufacturer.
 
  • #3
mfb said:
In general you can split your uncertainty into two components:
- systematic: you are wrong in the same way no matter how often you repeat the measurement. This can be a ruler that is too long or a poorly calibrated scale or similar things.
- statistical: you are wrong in a random way each measurement. You can often estimate this by taking multiple measurements. If that is not feasible you can use other, experiment-dependent approaches to estimate this uncertainty.
If in doubt, ask the manufacturer.

Thank you for your reply. When you say experiment-dependent approaches is there a standard for estimating uncertainty in this way?

EDIT: I just did a quick Wikipedia search and found that there are two types of uncertainty estimates; Type A and Type B. I suspect that the module I took described the Type A method whereas my question appears to be answered by the description of the Type B method. Can you confirm?

Also, is the calibration tolerance a measure of uncertainty in the same way that the manufacturer's stated accuracy is a measure of uncertainty? and are they systematic uncertainties, random uncertainties or a combination of both?
 
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  • #4
fonz said:
Thank you for your reply. When you say experiment-dependent approaches is there a standard for estimating uncertainty in this way?
It depends on the experiment and the analysis method, there is no rule that fits all (or even most) experiments.
fonz said:
I suspect that the module I took described the Type A method whereas my question appears to be answered by the description of the Type B method. Can you confirm?
Yes.
fonz said:
Also, is the calibration tolerance a measure of uncertainty in the same way that the manufacturer's stated accuracy is a measure of uncertainty?
Ask the manufacturer.
fonz said:
and are they systematic uncertainties, random uncertainties or a combination of both?
If you use the same scale for all measurements, a wrong scale will have the same deviation in every measurement (assuming the measurements are not done at completely different points of the scale). It is a systematic uncertainty.
 
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Likes fonz
  • #5
mfb said:
It depends on the experiment and the analysis method, there is no rule that fits all (or even most) experiments.Yes.
Ask the manufacturer.If you use the same scale for all measurements, a wrong scale will have the same deviation in every measurement (assuming the measurements are not done at completely different points of the scale). It is a systematic uncertainty.

Very helpful thank you.
 
  • #6
You may be able to estimate the error of an instrument if you understand how the instrument works.
If you are visually estimating a length against a set of graduations (like a ruler, or a graduated cylinder with liquid), the rule of thumb is that the error is 1/10 of a graduation. If the device is sensitive to electronics noise, you may be able to calculate the thermal noise in an amplifier and noise in a A/D converter.
If the device is a photon counting device, then your intensity measurement will have a shot noise component, proportional to sqrt(n). There may be other sources of noise that also contribute.
 

FAQ: Understanding Measurement Uncertainty: Calculating Accuracy and Precision

1. What is measurement uncertainty?

Measurement uncertainty refers to the degree of doubt or error present in a measurement due to limitations in the measurement process or equipment. It is an inherent characteristic of any measurement and can be influenced by various factors such as human error, equipment limitations, and environmental conditions.

2. Why is measurement uncertainty important?

Measurement uncertainty is important because it provides a measure of the reliability and accuracy of a measurement. It allows scientists to determine the range in which the true value of a measurement is likely to fall, and helps in making informed decisions based on the data collected.

3. How is measurement uncertainty calculated?

Measurement uncertainty is calculated by considering various sources of error and their respective contributions to the overall uncertainty. This can be done using statistical methods such as standard deviation, or through more complex calculations such as the GUM (Guide to the Expression of Uncertainty in Measurement) method.

4. Can measurement uncertainty be eliminated?

No, measurement uncertainty cannot be completely eliminated. However, it can be reduced by using more precise equipment, improving techniques, and minimizing sources of error. The goal is to minimize uncertainty to a level that is acceptable for the intended use of the measurement.

5. How does measurement uncertainty affect scientific results?

Measurement uncertainty can have a significant impact on the interpretation of scientific results. It is important to understand the level of uncertainty associated with a measurement in order to accurately interpret and compare data. Failure to account for measurement uncertainty can lead to incorrect conclusions and potentially misleading results.

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