Understanding Measurement Uncertainty: Calculating Accuracy and Precision

[fonz]

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?

 

[mfb]

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.

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.

 

[fonz]

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?

 

[mfb]

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.

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.

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.

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.

 

[fonz]

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.

 

[Khashishi]

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.