A formula approximating the effective degrees of freedom of a combined standard uncertainty: u_c to the fourth power divided by the sum, over all components, of each contribution to the fourth power divided by its own degrees of freedom. The result goes into the Student t-table to pick k for the chosen coverage probability. One dominant Type A term with few repeats drags the effective degrees of freedom down, while many well-known Type B terms push it toward infinity and k back toward 2.
Welch-Satterthwaite gives 6.8 effective degrees of freedom, round down to 6 and k is 2.52.
Always round the effective degrees of freedom down, never up, before looking up k.
Also heard as
- W-S formula
- Welch-Satterthwaite
Related terms
Degrees of freedom
A count of the independent information behind an uncertainty estimate, showing how reliable that estimate is.
Coverage factor
The multiplier applied to combined standard uncertainty to obtain expanded uncertainty, usually k = 2.
Student t-distribution
A bell-shaped distribution with heavier tails than the normal, used to set coverage factors when data are limited.
Combined standard uncertainty
The total standard uncertainty of a result, found by combining all input uncertainties through the measurement model.
Type A evaluation
Putting a number on an uncertainty component by running statistics on your own repeat readings.