error propagation

How Can Error Propagation be Quantified?

Error propagation can be quantified using statistical methods. The most common approach involves using the propagation of uncertainty formula, which combines the uncertainties of individual measurements to estimate the overall uncertainty in the calculated parameter. For a function Z that depends on variables X and Y, the propagated error can be calculated as:
\[ \sigma_Z = \sqrt{\left(\frac{\partial Z}{\partial X}\sigma_X\right)^2 + \left(\frac{\partial Z}{\partial Y}\sigma_Y\right)^2} \]
where \( \sigma_X \) and \( \sigma_Y \) are the standard deviations of X and Y, respectively.

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