https://doi.org/10.1351/goldbook.08095
Statistic, derived from a result reported by a participant in a proficiency testing scheme, used in interpretation of participant performance and to allow comparison with defined objectives.
Notes:
- The purpose of a performance score is to express the deviation of the reported value from the assigned value in a proficiency testing scheme in a manner that allows comparison with performance criteria.
- Names and defining equations of frequently used performance scores are listed in Table 1. Their definitions and interpretations are given in ISO/IEC 17043 and ISO 13528.
| Name | Symbol | Defining equation | Equation symbols |
|---|---|---|---|
| z score | z | \(z_{i} = \frac{x_{i} - x_{\rm{PT}}}{\sigma_{\rm{PT}}}\) | xi: ith reported value, xPT: assigned value. σPT: standard deviation for proficiency assessment. |
| z’ score z prime score | z’ | \(z_{i}' = \frac{x_{i} - x_{\rm{PT}}}{\sqrt{\sigma_{\rm{PT}}^{2} + u^{2}(x_{\rm{PT}})}}\) | u(xPT): standard measurement uncertainty of the assigned value. |
| ζ score zeta score | ζ | \(\zeta_{i} = \frac{x_{i} - x_{\rm{PT}}}{\sqrt{u^{2}(x_{i}) + u^{2}(x_{\rm{PT}})}}\) | u(xi): standard measurement uncertainty of the reported value. |
| En score En number | En | \(E_{n}(i) = \frac{x_{i} - x_{\rm{PT}}}{\sqrt{U^{2}(x_{i}) + U^{2}(x_{\rm{PT}})}}\) | U(xPT): expanded measurement uncertainty of the assigned value. (Usually with a coverage probability of approximately 95 %). U(xi): expanded measurement uncertainty of the participant’s result. (Usually with a coverage probability of approximately 95 %). |