Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Uncertainty Calculation for the Ratio of Dependent Measurements



C M. Wang, H K. Lyer, J Hannig


In this paper we consider the problem of computing an uncertainty interval a ratio with a prescribed confidence level. Although an exact confidence interval procedure, known as the Fieller interval, is available for this problem, practitioners often use various non-exact methods. One such non-exact method is based on the propagation of error approach described in the ISO Guide to the Expression of Uncertainty in Measurement to calculate the standard uncertainty. A confidence interval with presumed confidence level of 95% is obtained by using a coverage factor k = 2. We demonstrate that, using n-1 degrees of freedom for the standard uncertainty, and the corresponding coverage factor of the t table value, leads to uncertainty intervals which are nearly identical to Fieller's exact intervals whenever the measurement relative uncertainties are small. In addition, they are easy to compute and may be recommended for routine use in metrological applications.


coverage probability, fieller interval, ISO GUM, propagation of error


Wang, C. , Lyer, H. and Hannig, J. (2003), Uncertainty Calculation for the Ratio of Dependent Measurements, Metrologia (Accessed July 15, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created June 1, 2003, Updated February 17, 2017