What is Error propagation: Definition and 92 Discussions

In statistics, propagation of uncertainty (or propagation of error) is the effect of variables' uncertainties (or errors, more specifically random errors) on the uncertainty of a function based on them. When the variables are the values of experimental measurements they have uncertainties due to measurement limitations (e.g., instrument precision) which propagate due to the combination of variables in the function.
The uncertainty u can be expressed in a number of ways.
It may be defined by the absolute error Δx. Uncertainties can also be defined by the relative error (Δx)/x, which is usually written as a percentage.
Most commonly, the uncertainty on a quantity is quantified in terms of the standard deviation, σ, which is the positive square root of the variance. The value of a quantity and its error are then expressed as an interval x ± u. If the statistical probability distribution of the variable is known or can be assumed, it is possible to derive confidence limits to describe the region within which the true value of the variable may be found. For example, the 68% confidence limits for a one-dimensional variable belonging to a normal distribution are approximately ± one standard deviation σ from the central value x, which means that the region x ± σ will cover the true value in roughly 68% of cases.
If the uncertainties are correlated then covariance must be taken into account. Correlation can arise from two different sources. First, the measurement errors may be correlated. Second, when the underlying values are correlated across a population, the uncertainties in the group averages will be correlated.

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1. I Formula for the propagation of complex errors

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2. Error propagation leads to different uncertainties, which do I choose?

I understand how to compute and propagate errors but have trouble with conceptualizing all things put together. I have performed an experiment to determine a value for some quantity. This quantity depend on two variables. The first one depend in turn on some other quantities as well but I think...

50. Error Propagation and Uncertainties in Parameters

There is a quantity (W) that I would like to calculate that is, ultimately, a function of parameters that I can measure directly (a and b), W = W(a, b) But I cannot measure a and b perfectly, there will be some uncertainty in these measurements. This uncertainty will propagate into my...