Uncertainties/error propogation

  • Thread starter ElectricMile
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In summary, uncertainties/error propagation is the process of estimating the uncertainty in the output of a mathematical model or measurement based on the uncertainties in the input parameters. It is important in scientific research because it allows scientists to determine the reliability and accuracy of their results and identify sources of error. Uncertainties/error propagation is calculated using statistics and probability, considering the standard deviation of input parameters. Common sources of uncertainties in scientific experiments include instrumental and human errors, environmental variations, and limitations in measuring equipment. To minimize uncertainties, scientists can use high-quality equipment, perform multiple trials, and carefully control experimental conditions while accurately documenting and analyzing potential sources of error.
  • #1
ElectricMile
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i know the following:

q = x+y+z

ERROR IN q = sqrt((error in x^2)+(error in y^2)+(error in z^2))

but, what if the equation i have is

q = x+y-z

would it still be that same equation or would it be,


ERROR IN q = sqrt((error in x^2)+(error in y^2)-(error in z^2))
 
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  • #2
It would be the same equation, add the error
 
  • #3


The equation for uncertainty or error propagation would still be the same for q = x+y-z. The formula for calculating the error in q is based on the individual errors in x, y, and z, regardless of the signs (+ or -) in the original equation. This is because the error in a calculation is influenced by the magnitudes of the errors in each variable, not the signs.

However, it is important to note that the error in q = x+y-z may be different than the error in q = x+y+z due to the subtraction of the error in z. This can result in a smaller or larger error in q, depending on the magnitude of the error in z. It is always important to carefully consider the signs and magnitudes of the errors in each variable when calculating error propagation.
 

1. What is uncertainties/error propagation?

Uncertainties/error propagation is the process of estimating the uncertainty in the output of a mathematical model or measurement based on the uncertainties in the input parameters.

2. Why is uncertainties/error propagation important in scientific research?

Uncertainties/error propagation is important because it allows scientists to determine the reliability and accuracy of their results. It also helps to identify the most significant sources of error in their experiments or models.

3. How is uncertainties/error propagation calculated?

Uncertainties/error propagation is calculated using the principles of statistics and probability. It involves determining the standard deviation of the input parameters and then using mathematical formulas to propagate this uncertainty to the output.

4. What are some common sources of uncertainties in scientific experiments?

Common sources of uncertainties in scientific experiments include instrumental errors, human errors, environmental variations, and limitations in measuring equipment.

5. How can uncertainties be minimized in scientific research?

Uncertainties can be minimized in scientific research by using high-quality equipment, performing multiple trials, and carefully controlling experimental conditions. It is also important to accurately document and analyze any potential sources of error.

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