Proficiency tests with uncertainty information: Extension of the En number for cases with no reference laboratory

When measurement uncertainties are reported in a proficiency test (PT), the performances are usually evaluated through a comparison with the measurement result of a reference laboratory as set forth in the ISO 13528 standard. On the other hand, the standard does not specify a performance evaluation method when there is no reference laboratory. In this study, the En number, which is described in ISO 13528 as one of the performance statistics, is reinterpreted as an index for Bayesian posterior predictive checking, and extended to a case with no reference laboratory. This extended En number proposed in this study has clear statistical meaning and is easy to compute.