performance score

synonym: performance statistic
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:
  1. 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.
  2. 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.
Table 1 Examples of performance scores used in proficiency testing.
NameSymbolDefining equationEquation symbols
z scorez\(z_{i} = \frac{x_{i} - x_{\rm{PT}}}{\sigma_{\rm{PT}}}\)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 %).
Source:
PAC, 2021, 93, 997. 'Metrological and quality concepts in analytical chemistry (IUPAC Recommendations 2021)' on page 1031 (https://doi.org/10.1515/pac-2019-0819)