This free proficiency testing z-score calculator scores your PT result the same way a scheme provider does. Enter your laboratory result and the PT scheme’s assigned value to get all four standard performance scores (z, z′, ζ and En) in one go, each with an ISO 13528 verdict. Useful when checking a PT report or preparing corrective action records for ISO/IEC 17025.
How to use the Proficiency Testing Z-Score Calculator
- Enter your laboratory result (x) and the assigned value (X).
- Enter the standard deviation for proficiency assessment (σpt) from the PT report.
- Add the standard uncertainty of the assigned value and your own standard uncertainty to get z′, zeta and En.
- Set the coverage factor k for En and press Calculate scores.
Each score from the proficiency testing z-score calculator comes with an ISO 13528 verdict: satisfactory, questionable or unsatisfactory. The Eurachem guides on proficiency testing explain how to follow up each type of score.
Which proficiency testing score should you use?
- z-score: the standard score when the scheme gives a σpt and the assigned value’s uncertainty is small (u(X) ≤ 0.3 σpt).
- z′-score: use when the assigned value’s uncertainty is not negligible. It widens the denominator so labs are not penalised for a poorly known assigned value.
- ζ (zeta) score: tests whether your result agrees with the assigned value within your claimed uncertainty. It helps check whether your uncertainty estimates are realistic.
- En number: the same idea as zeta but with expanded uncertainties. It is common in calibration PT and inter-laboratory comparisons.
Interpretation (ISO 13528 / ISO/IEC 17043)
| Score | Satisfactory | Questionable | Unsatisfactory |
|---|---|---|---|
| z, z′, ζ | |score| ≤ 2.0 | 2.0 < |score| < 3.0 | |score| ≥ 3.0 |
| En | |En| ≤ 1.0 | — | |En| > 1.0 |
What to do with a questionable or unsatisfactory score
- Check for transcription and unit errors first. These cause a large share of PT failures.
- Review calculation, dilution factors, moisture or dry-weight corrections and reporting basis.
- Check calibration, reference material, instrument performance and QC charts from the same period.
- Look at trends across rounds. Two consecutive questionable scores on the same side usually need the same action as one unsatisfactory score.
- Document the root cause, correction, corrective action and effectiveness check.
Frequently asked questions
What is a good z-score in proficiency testing?
A z-score between −2 and +2 is satisfactory. Between 2 and 3 (either sign) is questionable and worth reviewing. 3 or above is unsatisfactory and normally requires corrective action.
What is the difference between the z-score and the En number?
The z-score compares your error with a fixed standard deviation set by the PT provider. The En number compares it with the combined expanded uncertainty of your result and the reference value, so it also tests your uncertainty claim.
Where do I find σpt and u(X)?
Both are normally stated in the PT provider’s final report for each test item. If σpt is not given, some schemes derive it from the Horwitz equation. You can use our HorRat calculator to estimate it.
Can a result have a good z-score but a bad zeta score?
Yes. If you claim a very small uncertainty, a result close to the assigned value can still fail the zeta test. This is a sign your uncertainty estimate may be too optimistic.
How is a z-score interpreted?
|z| ≤ 2.0 is satisfactory, 2.0 < |z| < 3.0 is questionable (a warning signal) and |z| ≥ 3.0 is unsatisfactory (an action signal). The sign shows whether your result is above or below the assigned value.
What is the En number formula?
En = (x − X) ÷ √(Ulab² + Uref²), using expanded uncertainties (usually k = 2). |En| ≤ 1.0 is satisfactory and |En| > 1.0 is unsatisfactory.
Related tools
Results are estimates for general information. Check critical decisions with a qualified professional.