Error propagation and standard deviation

In summary, the conversation discussed the topic of error propagation and standard deviation in relation to experimental physics. The individual was seeking guidance on how to include errors in the standard deviation when determining the difference between measured and theoretical values. They were recommended to check Kline and McClintock's 1953 paper on uncertainty analysis, as well as the NIST guidelines and the GUM for more current information on the topic. The GUM was noted as being a particularly readable and informative resource.
  • #1
Sral2018
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Hey there,
First time on this forums, looking forward to some interesting discussions :)
I am currently trying grasp the concepts of error propagation and standard deviation in relation to experimental physics. I have some data set and i want to determine the difference between the measured and theoretical values including errors and how reliable my reading are. My problem is how do i include these errors in the standard deviation?
 
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  • #2
You might check Kline and McClintock's 1953 paper on uncertainty analysis. It is a standard in the field.
 
  • #3
There is also the NIST guidelines which are a little more up to date.

https://www.nist.gov/sites/default/files/documents/2017/05/09/tn1297s.pdf
 
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1. What is error propagation and why is it important in scientific experiments?

Error propagation is the process of quantifying and analyzing the uncertainties and errors associated with experimental measurements. It is important in scientific experiments because it allows researchers to understand the reliability and accuracy of their results, and to make more informed conclusions based on the data.

2. How is error propagation related to standard deviation?

Standard deviation is a statistical measure of the spread of data points around the mean value. It is commonly used in error propagation calculations to quantify the uncertainty or variability in a set of experimental measurements. A larger standard deviation indicates a higher degree of uncertainty in the data, while a smaller standard deviation indicates a more precise and reliable set of measurements.

3. What factors can contribute to error propagation?

There are several factors that can contribute to error propagation, including measurement errors, systematic errors, and random errors. Measurement errors can result from limitations in the instruments used, while systematic errors can arise from flaws in the experimental design or procedures. Random errors are inherent in any measurement and cannot be eliminated, but they can be reduced through careful experimental techniques.

4. How is error propagation calculated?

Error propagation calculations involve using mathematical equations to determine how uncertainties in one or more measurements affect the overall uncertainty in the final result. This is done by propagating the individual uncertainties through the relevant equations and combining them using statistical methods, such as the propagation of uncertainty formula.

5. How can we minimize error propagation in scientific experiments?

To minimize error propagation, it is important to use precise and accurate instruments, carefully design and execute experiments, and repeat measurements multiple times to reduce the effects of random errors. It is also crucial to properly analyze and interpret the data, and to report the uncertainties associated with the results. Communicating and discussing the potential sources of error with other scientists can also help to minimize error propagation in future experiments.

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