What the coverage factor k means
The coverage factor multiplies the combined standard uncertainty to give an expanded uncertainty with a stated level of confidence. k = 2 is roughly 95 % for a normal distribution.
A combined standard uncertainty u_c corresponds to about 68 % coverage for a normal distribution — too small an interval for most practical statements. The expanded uncertainty U = k·u_c widens it: k = 2 gives roughly 95 %, k = 3 roughly 99.7 %.
When k = 2 is not 95 %
If the combined uncertainty is dominated by a single rectangular component, or the Type A evaluation is based on very few observations, the output distribution is not normal and k = 2 may not deliver 95 %. The GUM's Welch–Satterthwaite formula for effective degrees of freedom, or a Monte Carlo evaluation, addresses this.
Reading certificates
An uncertainty quoted without k cannot be compared with one quoted at k = 2. Ask for it; accredited certificates are required to state it.
Frequently asked questions
- Why do some certificates quote k = 2.1 or 2.3?
- Because the effective degrees of freedom were low and the laboratory used the t-distribution to achieve 95 % coverage rather than assuming normality.
- Can I convert U at k = 2 to a standard uncertainty?
- Yes: divide by k. U = 0.04 °C at k = 2 gives u = 0.02 °C.
References
- [1]JCGM 100:2008 — Guide to the expression of uncertainty in measurement (GUM)
General technical guidance written against the cited sources. It is not regulatory or legal advice and does not replace the applicable standard, guideline or a qualified reviewer's judgement.
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