The formula
- xlab: the value your lab reports.
- xref: the reference (assigned) value from the PT provider.
- Ulab and Uref: the expanded uncertainties of each value, normally at k = 2 (about 95% coverage).
An absolute En below 1 means the difference is covered by the combined uncertainty, which is a satisfactory result. An |En| of 1 or more is unsatisfactory: either the measurement is off, or the uncertainty is too small to cover it. The sign tells you the direction. A positive En means you read high, and a negative En means you read low.
Worked example: a 200 g weight
The reference value of a PT weight is 200.0003 g with Uref = 0.2 mg. Two labs both report 200.0006 g, a 0.3 mg difference, but they claim different uncertainties.
| Participant | En | Result |
|---|---|---|
| Lab A reports U = 0.3 mg | 0.832 | Satisfactory |
| Lab B reports U = 0.1 mg | 1.342 | Unsatisfactory |
Same reading, different outcome. Lab B's claimed uncertainty is smaller than its real measurement capability. This is why a PT checks your uncertainty budget as much as your technique.
What to check when |En| is 1 or more
- Transcription and units: a misplaced decimal, g vs. mg, or the wrong test point.
- Reference standards: calibration status, drift since the last calibration, and correct use of the values on their certificates.
- Environment: temperature stability, drafts, and acclimation time, which matter most for mass and balance work.
- Procedure: whether the technician followed the documented method, and whether the method fits the artifact.
- Uncertainty budget: missing contributors such as repeatability, resolution, reference drift, or air buoyancy, and the coverage factor used.
Record the investigation and corrective action, and check whether any customer calibrations made the same way are affected. See ISO/IEC 17025 PT requirements for how this fits your quality system.
PT vs. interlaboratory comparison
An interlaboratory comparison (ILC) is any organized comparison of measurements on the same items by two or more labs, and En numbers are a common way to score one. Proficiency testing is an ILC run by a provider that evaluates each participant against pre-set criteria. Lake Balance is accredited by PJLA as a proficiency testing provider to ISO/IEC 17043:2023 (certificate L24-898), and each participant result is scored against our reference value.