## Missing uncertainties

Sometimes uncertainties are not reported with the concentration measurements, usually when the data were submitted before the reporting of uncertainties became mandatory. In such cases, the uncertainties are estimated using fixed and relative standard deviations derived from the uncertainties that have been reported to the ICES data base (extraction date: 15 February 2019).

Suppose $$c$$ is a concentration reported with missing uncertainty. Then the uncertainty $$u$$ is estimated from:

$u^2 = s^2 + f^2 v^2 c^2$

where:

• $$s$$ is the fixed standard deviation, taken to be one third of the detection limit when reported, and otherwise the value estimated from the uncertainties in the ICES database
• $$v$$ is the relative standard deviation, estimated from the uncertainties in the ICES database
• $$f$$ is an inflation factor, based on available quality assurance information, that increases the relative error if analytical performance is poor

The inflation factors are based on QUASIMEME Z-scores supplied to ICES on CD by analytical laboratories and Certified Reference Material (CRM) concentrations held in the ICES database. The CRM concentrations (for the relevant contaminant, matrix and year) are converted to Z-scores

$Z_i = \frac {M_i-A_i} {0.125A_i}$

where $$M_i$$ are the measured concentrations and $$A_i$$ are the certified reference values. These are then combined with the QUASIMEME Z-scores (for the contaminant, matrix and year) to give

$f^2 = \frac {1} {n} \sum_i Z_i^2$

where $$n$$ is the total number of Z-scores. In practice, Z-scores that are large (possibly due to unit misreporting) can unduly influence the inflation factors, so are truncated at 3, leading to a maximum inflation factor of 3. The inflation factors are also truncated below at 1, since this corresponds to good analytical performance. If there is no quality assurance information (for the contaminant, matrix and year), the inflation factors are set to 3.

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