Proficiency testing is a key tool to assess the technical competence of testing laboratories. One of the most widely used statistical methods to interpret the results of these programs is the z-score, a metric that helps identify significant deviations from the assigned reference value.
In laboratory quality assessment, Ring Trials (interlaboratory comparisons) and Proficiency Testing (competency evaluations) serve to compare results across different laboratories. While both aim to enhance accuracy and reliability, they differ in their objectives, methodologies, and applications.
Ring Trials focus on method harmonization and validation, whereas Proficiency Testing is designed to assess the technical competence of participating laboratories.
To learn more, we invite you to read our latest article: Comparison Between Ring Trials and Proficiency Testing.
However, obtaining an unsatisfactory z-score should not be viewed simply as a failure, but rather as a valuable opportunity for improvement. In this article, we explore in depth what a z-score is, how to interpret it properly according to the ISO 13528:2022 standard, and what actions a laboratory should take after receiving an unsatisfactory result.
What is a z-score in proficiency testing?
A z-score is a statistical index that expresses the difference between the result reported by the laboratory and the assigned value by the organizer of the proficiency test, relative to the standard deviation of the study. It is calculated with the following formula:
z = (x – μ) / σ
Where:
- x: result reported by the laboratory
- μ: assigned value (reference value)
- σ: standard deviation for performance assessment
A z-score provides a measure of how far a result is from the expected value. It is widely accepted in interlaboratory programs due to its simplicity and interpretative power.
Interpretation of z-score results
According to ISO 13528:2022, typical evaluation criteria for z-scores are:
- 0 ≤ z-score < 2: Satisfactory result
- 2 ≤ z-score ≤ 3: Questionable result
- z-score > 3: Unsatisfactory result
These reference values allow objective classification of laboratory performance and help in making informed decisions. Below is a graphical representation of how we present the results in our programs:
What a high z-score indicates in proficiency testing?
A z-score greater than or equal to 3 (or less than or equal to -3) means that the laboratory’s result is significantly far from the assigned value. This may indicate:
- Systematic errors or methodological bias.
- Sample preparation or analysis issues.
- Poorly estimated uncertainties.
- Calibration or personnel issues.
ISO 13528 emphasizes that test organizers must adequately inform participants and that participants must implement documented corrective actions.
Common causes of unsatisfactory results
Some of the most common causes for a z-score result z-score > 3 include:
- Use of a non-validated analytical method.
- Human errors during testing.
- Poorly calibrated equipment.
- Data transcription mistakes.
- Misinterpretation of test instructions.
In all cases, a root cause analysis approach is essential, such as the “5 Whys” method or Ishikawa diagrams.
Recommended actions for unsatisfactory results
ISO 13528 recommends that laboratories receiving unsatisfactory results:
- Seek support from your proficiency testing provider—they can assist you in identifying deviations and helping you mitigate them.
- Document the result in their quality records.
- Conduct a root cause analysis of the deviation.
- Implement corrective and preventive actions (CAPA).
- Verify the effectiveness of the implemented actions.
- Maintain traceability of any changes applied to the method or system.
This process is essential not only to meet regulatory requirements (such as those from ISO/IEC 17025), but also to demonstrate commitment to continuous improvement.
ISO 13528 Considerations on performance evaluation
ISO 13528:2022, “Statistical methods for use in proficiency testing by interlaboratory comparison,” establishes guidelines for applying statistical methods in such studies. Regarding z-score usage, the standard specifies:
- The assigned value μ should have negligible or well-defined uncertainty.
- The standard deviation σ should appropriately represent the expected interlaboratory variability.
- If the assigned value has significant uncertainty, the z-score can be used, incorporating this uncertainty into the formula:
z = (x – X) / √(σ² + uₓ²)
Where uₓ is the uncertainty associated with the assigned value.
Additionally, the standard states that performance evaluations must be communicated clearly and that proficiency test organizers must provide technical support when necessary.
Z-Score vs. Other Evaluation Criteria
Although the z-score is the most common, ISO 13528 also considers other evaluation methods such as:
- z-score: when the assigned value has significant uncertainty.
- En-score: used when both the laboratory and assigned value have known uncertainties.
- Robust statistics: such as median or MAD, useful for highly dispersed data or outliers.
Choosing the appropriate criterion depends on the type of study, amount of data, and objective of the interlaboratory comparison.
What to do if a client requests clarification?
During accreditation audits or client evaluations, a customer may request clarification on an unsatisfactory result. In that case, the laboratory should:
- Provide a clear technical explanation.
- Show evidence of root cause analysis.
- Present the corrective actions implemented.
- Ensure traceability and reliability have been restored.
A transparent and proactive management approach strengthens the client’s trust in the lab’s quality.
Best practices to minimize unsatisfactory results
- Provide ongoing training to staff.
- Use validated methods and regularly verify their performance.
- Frequently participate in proficiency testing.
- Internally review results before submission.
- Ensure traceability of equipment and instruments.
These practices not only improve performance in interlaboratory programs but also enhance overall laboratory quality.
How can SHAPYPRO help you?
At SHAPYPRO, we are leaders in organizing ISO/IEC 17043 accredited proficiency testing programs. We also provide:
- Technical support in interpreting results.
- Figure out deviations and mitigate them
- Detailed reports with statistical analysis.
- Assistance with defining corrective actions.
- Recommendations based on ISO 13528.
📩 Contact us to learn more about our programs and technical support.
You can also check our article on how to interpret proficiency testing results for more insights.
Conclusion
The z-score is a powerful tool for evaluating proficiency testing performance, but its true value lies in how the results are interpreted and managed. An unsatisfactory result should not be seen as a threat but as a chance for growth and improvement.
Correctly applying the recommendations of ISO 13528 allows laboratories to reinforce their technical competence and maintain their commitment to quality.