# Introduction to sensitivity coefficients

## Introduction to sensitivity coefficients

Sensitivity coefficients provide a measure of how sensitive the measurand (Y) is to a change in given input quantity (X_i).

Simply put, a sensitivity coefficient answers the question: “How much does a change in this input quantity change the final measured value”?

In the process of uncertainty evaluation, sensitivity coefficients are used to translate the standard uncertainty associated with a given effect, u(x_i), into an uncertainty associated with the measurand. This is done by multiplying the standard uncertainty by the sensitivity coefficient. Note that the unit of a sensitivity coefficient is such that when the input quantity (with its associated unit) is multiplied by the sensitivity coefficient, then the result has the unit of the measurand. If the output quantity and the input quantity have the same unit, then the sensitivity coefficient will be dimensionless.

There are three ways in which sensitivity coefficients can be determined:

• Mathematically
• Numerically
• Experimentally

All three of these methods are equally valid and are all approved by the ‘Guide to the Expression of Uncertainty in Measurement’ (the GUM). Consequently, in a real-life uncertainty evaluation, it is possible that all three methods will be used. Each of these methods is examined in detail on the next page.