Question

What is the difference between propagation of error and propagation of uncertainty. Or are they the same thing?Please explain and what equations must I use.

Answer 1

propagation of error and propagation of uncertainty are the same thing.

Propagation of uncertainty (or propagation of error) is the effect of variables' uncertainties on the uncertainty of a function based on them. Uncertainties can also be defined by the relative error (Δx)/x

1. If x and y have independent random errors δx and δy, then the error in z = x + y is

δz = (δx² + δy²)^1/2.

2. If x and y have independent random errors δx and δy, then the error in z = x × y is

Δz/ z = {(δx/x)² + (δy/y)²}^1/2

3. If z = f(x) for some function f(), then δz = |f ‘ (x)| δx.