Expanded Uncertainty
Definition
The combined standard uncertainty multiplied by a coverage factor k, chosen to achieve a stated coverage probability. For a normal distribution, k = 2 gives approximately 95 percent coverage. Reported as U = k × u_c alongside the measurement result.
- Formula
- U = k x u_c, where u_c is combined standard uncertainty
- Typical k for ~95%
- k = 2 for a normal distribution
- Reporting standard
- ISO/IEC 17025 and GUM require U reported with the result
- Context
- Used in quantitative forensic measurements, e.g. toxicology, ballistics
Common questions
Why use k=2 instead of just reporting the standard uncertainty?+
Standard uncertainty alone covers only about 68 percent of the likely range of true values under a normal distribution. Multiplying by a coverage factor widens the interval to a level, commonly 95 percent, that is more meaningful for legal and quality decisions.
Does a larger expanded uncertainty mean the measurement is wrong?+
No. It reflects the combined effect of all identified uncertainty sources, such as calibration, repeatability, and matrix effects, at a stated confidence level. A sound method can still report a wide U if its inputs are genuinely variable.
How does expanded uncertainty differ from measurement error?+
Error is the usually unknown difference between a measured value and the true value. Expanded uncertainty is a calculated interval, derived from known variability sources, within which the true value is expected to fall at a stated probability.
Related terms
- Combined Standard Uncertainty
- The overall standard uncertainty of a result, obtained by combining all Type A and Type B component uncertainties in quadrature (square root...
- GUM
- Guide to the Expression of Uncertainty in Measurement. The international standard, maintained by eight metrology and standardisation bodies, that defines Type A...
- Type a Uncertainty
- Uncertainty evaluated by statistical analysis of a series of observations. The standard uncertainty is the standard deviation of the mean (standard error)...
- Type B Uncertainty
- Uncertainty evaluated by means other than statistical analysis of repeated measurements. Sources include calibration certificates, instrument specifications, reference data, and expert scientific...
- Z-Score (Proficiency Testing)
- A performance statistic in PT defined as z = (x - X) / s_PT, where x is the laboratory's result, X is...