Error Propagation

Abstract

Error is not a mistake in science. A mistake can be due to an incorrect entry of data in an experiment or an incorrect calculation. Error refers to the precision (uncertainty) of measurements, which one obtains by estimating the standard deviation of repetitive measurements of a certain parameter. We often use “the method of error propagation” to determine uncertainty (error) in a dependent variable from the measured uncertainty in the independent variables. Here, we discuss the origin of the error propagation equation and the assumptions considered to derive it. Intuitional notion of error propagation in statistics suggests that random relative error in the dependent variable cannot be less than the sum of those in the independent variable(s). In this article, we explain that some transcendental functions (such as trigonometric and log functions), however, do not follow this notion of error propagation because their first partial derivatives are usually small in magnitude and sometimes vanish completely at certain points. We further explain and discuss the behaviour of such a function. We have made suggestions for estimating errors in such non-linear functions.