Question about uncertainties

In summary, the original uncertainties in the independent variables can decrease in the propagated uncertainty if the random variables are independent and the derivatives of the function are small. This can be seen in the formula for calculating the error in a function of multiple independent variables, where the error is the square root of the sum of the squares of the individual errors.
  • #1
kodek64
8
0
(First post. Go easy on me, mods :D)
EDIT: Seems I got the wrong forum. If a mod could be so kind to move it, I'd appreciate it :P

Hi everyone!

I'm working on a formal lab report for my physics class, and after propagating my uncertainties into a formula, I got an even smaller uncertainty relative to the original uncertainties (one of the indep. variables was 9% while my propagated uncertainty was 6%)

Is this possible in ANY case?

If it's not, I will post more information about the equations I'm using. I already spent 2 hours looking at all the numbers and using mathematica to calculate the results for me, and I just don't know what could be wrong with it (if there's even anything wrong with it).

Thanks for your help,

KodeK
 
Last edited:
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  • #2
Is this possible in ANY case?
Yes. In general if the random variables are independent, the uncertainties tend to smooth out.
 
  • #3
mathman said:
Yes. In general if the random variables are independent, the uncertainties tend to smooth out.

Hmm, I'd like to show you the equations I'm using just to get an okay so I know I'm doing this right. How would I copy mathematica's LaTeX output and paste it on the site? I don't want to have to copy an in-line equation :P
 
  • #5
Yes, the errors can become less if the derivatives are small. If you evaluate a function f of independent variables x1, x2, ..., with respective errors dx1, dx2, ..., then the error in f is:

df = sqrt[df1^2 + df2^2 + ...]

where

df1 = f(x1 + dx1/2, x2,...) - f(x1 - dx1/2, x2,...)


df2 = f(x1, x2+dx2/2,...) - f(x1, x2 - dx2/2,...)

etc.
 

1. What are uncertainties in scientific research?

Uncertainties in scientific research refer to the potential errors or variations in data or measurements that may affect the accuracy and reliability of the results.

2. How do scientists account for uncertainties in their experiments?

Scientists account for uncertainties by conducting multiple trials, using standardized measurement techniques, and including error bars in their data analysis.

3. Why is it important to consider uncertainties in scientific research?

Considering uncertainties is important because it allows for a more accurate and realistic representation of the data, and helps to identify potential sources of error and improve the validity of the results.

4. How do uncertainties impact the interpretation of scientific findings?

Uncertainties can impact the interpretation of scientific findings by introducing a level of uncertainty or doubt in the results. This may require the researcher to further investigate or refine their methods to improve the accuracy of the findings.

5. Can uncertainties be completely eliminated in scientific research?

No, uncertainties cannot be completely eliminated in scientific research. However, they can be minimized through careful experimental design, precise measurements, and thorough data analysis.

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