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: 9 January 2023).

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

\[u^2 = s^2 + v^2 c^2\]

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 database¹
• \(v\) is the relative standard deviation, estimated from the uncertainties in the ICES database

¹ The detection limits reported to the ICES data base are sometimes unreliable. Basing \(s\) on one third of the detection limit (when reported) can therefore sometimes yield implausible uncertainties. To provide some robustness a more complicated procedure has evolved which involves the fixed standard deviation estimated from the uncertainties in the ICES data base, the detection limit, the quantification limit, the quality flag, and the measured concentration:

• if quality flag = D then \(s\) is taken to be one third of the detection limit
• else if quality flag = Q then \(s\) is taken to be one tenth of the quantification limit
• else if quality flag = < then \(s\) is taken to be the minimum of one third of the reported concentration and the fixed standard deviation estimated from the ICES database
• else \(s\) is taken to be the minimum of one third of the detection limit, one tenth of the quantification limit, one third of the reported concentration and the fixed standard deviation estimated from the ICES database↩︎