Proficiency Testing Calculator: z-Score, En and Zeta

A free calculator for evaluating proficiency testing (PT) and interlaboratory comparison (ILC) results. Calculate the z-score, z′, zeta and En number for a single result, or the robust mean, standard deviation and all z-scores from participant results with ISO 13528 Algorithm A. Calculations run in your browser; your data is not sent anywhere.

Laboratory result (x)

Assigned value (X)

σ_pt

u_X (optional, for z′)

z = (x − X) / σ_pt · z′ = (x − X) / √(σ_pt² + u_X²)

Laboratory result (x)

Assigned value (X)

u_lab (standard)

u_X (standard)

ζ = (x − X) / √(u_lab² + u_X²)

Laboratory result (x)

Reference value (X)

U_lab (expanded)

U_ref (expanded)

E_n = (x − X) / √(U_lab² + U_ref²)

Participant results (one value per line; optionally "Code;value")

σ_pt (if empty, robust s* is used)

How to interpret the results

z, z′ and ζ: |value| ≤ 2 satisfactory, between 2 and 3 questionable (warning signal), ≥ 3 unsatisfactory (action signal).
En: |En| ≤ 1 satisfactory, |En| > 1 unsatisfactory.
The criteria in the scheme protocol always apply; some providers use different limits.

For a detailed explanation of the formulas with numerical examples, see our proficiency testing guide.

Frequently Asked Questions

How is a z-score calculated?
z = (x − X) / σpt, where x is the laboratory result, X the assigned value and σpt the standard deviation for proficiency assessment. |z| ≤ 2 is satisfactory, 2 < |z| < 3 questionable and |z| ≥ 3 unsatisfactory.

How is the En number calculated?
En = (x − X) / √(U_lab² + U_ref²), where U are expanded uncertainties (usually k=2). |En| ≤ 1 is satisfactory and |En| > 1 unsatisfactory. It is the most common statistic in calibration comparisons.

What is the difference between z′ and zeta?
z′ is used when the uncertainty of the assigned value is not negligible: z′ = (x − X) / √(σpt² + u_X²). Zeta uses the laboratory's own standard uncertainty: ζ = (x − X) / √(u_lab² + u_X²), and shows whether the stated uncertainty is consistent with the result.

What is Algorithm A?
A robust method defined in ISO 13528 for calculating a mean and standard deviation that are not distorted by outliers. It is often used when the consensus of participants is taken as the assigned value.

Is my data sent anywhere?
No. All calculations run in your browser; the values you enter are not sent to a server or stored.

Do you run proficiency testing schemes?

YT-LAK manages protocols, applications, quotations, sample circulation, result collection, z-score, En and consensus evaluation, and reporting in one system.

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