Proficiency Testing: reading En and z scores

Your own calibration says your result is right. Proficiency testing is how you prove it from the outside — by measuring the same item as other labs and being scored against an independent assigned value. The two numbers that matter are the z-score and the E_n number, and they answer different questions.

What proficiency testing is

A proficiency testing (PT) scheme — also called an interlaboratory comparison (ILC) — sends the same artefact or sample to many laboratories. Each lab measures it blind, reports a value (with its uncertainty), and the scheme provider compares everyone against a single assigned value. It is external, independent evidence that your measurements agree with the wider metrology community, and ISO/IEC 17025 (clause 7.7) expects accredited labs to take part.

One delivery of an item and its scoring is a round. Over several rounds you build a track record — which is exactly what an assessor wants to see.

The assigned value and its uncertainty

Everything is measured against the assigned value (X) — the scheme’s best estimate of the truth for that item, with its own uncertainty U_ref. It may come from a reference laboratory, a certified reference material, or a robust average of all participants. Your job is to land close to X; the scoring tells you how close is close enough.

The z-score: how far out are you?

The z-score compares your deviation from the assigned value to a target spread the scheme sets, called the standard deviation for proficiency assessment (sigma, σ_pt):

z = (x − X) / σ_pt

where x is your reported value. The interpretation is fixed by ISO 13528:

• |z| ≤ 2 — Satisfactory. No action needed.
• 2 < |z| < 3 — Questionable (a warning signal). Worth a look.
• |z| ≥ 3 — Unsatisfactory (an action signal). Investigate.

The z-score measures performance against a chosen spread. It does not use your own claimed uncertainty — so it tells you whether you are close, but not whether your uncertainty statement is believable.

The En number: is your uncertainty honest?

The E_n number is the one used in calibration ILCs, because it puts your uncertainty on trial. It scales your deviation by the combined uncertainty of your result and the reference:

E_n = (x − X) / √(U_lab² + U_ref²)

• |E_n| ≤ 1 — Satisfactory: your result agrees with the assigned value within the uncertainties.
• |E_n| > 1 — Unsatisfactory: the gap is bigger than your combined uncertainty can explain.

This is the subtle part. An E_n above 1 means one of two things: your result is genuinely off, or you have under-stated your uncertainty. A lab that quietly inflates its uncertainty can pass E_n while hiding a real bias — which is why assessors read E_n alongside the actual deviation, not on its own.

z or En — which one?

Use the score the scheme reports, but know what each is telling you. z answers “am I close to everyone else?”; E_n answers “is my measurement and my uncertainty claim defensible?”. For accredited calibration, E_n is usually the headline number; for testing schemes, z (and its cousin z’) is more common. When you have both, take the worse of the two as your overall verdict.

A z of 0.3 with an E_n of 1.8 is not a pass — it means you were close by luck, but your uncertainty budget is too small to back it up.

When a result is unsatisfactory

A Questionable or Unsatisfactory score is not a failure to hide — it is a finding to work. Treat it as a nonconformance: check for transcription and unit errors first, then review the standard used, the method, the environment and the uncertainty budget. Record the investigation, the root cause and the corrective action, and re-evaluate. A documented recovery from a bad round is stronger evidence of a healthy lab than a clean sheet with no trail.

Where it fits

Proficiency testing closes the loop that internal checks cannot: traceability proves your chain to the SI, intermediate checks prove stability between calibrations, and PT proves agreement with the outside world. Keeping the schemes, rounds, scores and resulting actions in the same system as your calibrations turns “we participate in PT” into evidence you can hand an assessor in one report.

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