Propagation of error:
In statistics, propagation of error is the effect of variables' uncertainties on the uncertainty of a function based on them. At the time when the variables are the values of experimental measurements they have uncertainties because of measurement limitations which propagate to the combination of variables in the function.
The uncertainty can be usually defined by the absolute error. Uncertainties can be defined by the relative error which is usually percentage error.
Commonly the error on a quantity is given as the standard deviation, σ. Standard deviation is positive square root of the variance, σ2 .
Error estimates for non-linear functions are biased on the account of using truncated series expansion. The extent of this bias relies on the nature of the function.
In data-fitting applications it is possible to assume that measurements errors are uncorrelated. Nevertheless, parameters derived from these measurements, like least-squares parameters, will be correlated. For instance, in linear regression, the errors on slope and intercept will be correlated and the term with the correlation coefficient, ρ, can make a significant contribution to the error on a calculated value.
If the result of a measurement is to have meaning it cannot consist of only the measured value. An indication of how accurate the result should be included also. Indeed, characteristically more effort is required to determine the error or uncertainty in a measurement than to perform the measurement itself. Therefore, the result of any physical measurement has 2 significant components:
(1) A numerical value giving the best estimate possible of the quantity measured, and
(2) the degree of uncertainty associated with the estimated value of it.