Kacker, R.
(2006),
Bayesian Alternative to the Guide's Use of the Welch-Satterthwaite Formula, Metrologia, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=150900
(Accessed May 22, 2025)
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.
Bayesian Alternative to the Guide's Use of the Welch-Satterthwaite Formula
Published
Author(s)
Abstract
The Guide to the Expression of Uncertainty in Measurement suggests that to account for the statistical uncertainty in a combined standard uncertainty that arises when one or more of its components are evaluated from a limited number of independent normally distributed measurements, the coverage factor may be determined from a scaled-and-shifted t-distribution with effective degrees of freedom obtained from the Welch-Satterthwaite formula. We propose, as an alternative, a normal distribution with standard deviation equal to a Bayesian combined standard uncertainty. A Bayesian combined standard uncertainty has no statistical uncertainty arising from limited numbers of measurements. Therefore, the proposed normal distribution with Bayesian combined standard uncertainty greatly simplifies the expression of uncertainty by eliminating the need of quantifying the statistical uncertainty in uncertainty arising from limited numbers of measurements.Citation
Metrologia
Volume
43
Pub Type
Journals
Download Paper
Keywords
Behrens-Fisher distribution, measurement uncertainty, t-distribution, variance components
Citation
Issues
If you have any questions about this publication or are having problems accessing it, please contact [email protected].
Created January 3, 2006, Updated February 19, 2017