How do I compare my result with the certified values?
The underlying principle is that one has to check whether the difference between the measured result and the certified value is larger than the expanded combined uncertainty of measurement and certified value. This is done as follows:
- Calculate the standard uncertainty of the certified value (uCRM). This is obtained by dividing the expanded uncertainty given on the certificate by the expansion factor (also stated on the certificate).
- Estimate the measurement uncertainty (um) of the result. As a very rough approximation, the reproducibility standard deviation can be used
- Combine the two uncertainties:
- Check whether 2*uc is larger than the difference between the certified and the measurement value. If this is the case, the measurement result agrees within the limits of the respective uncertainties with the certified values
For example: Certified reference material BCR-605 (road dust) with a trimethyllead-content of 7.9 ± 1.2 µg/kg has been used. The analytical result was 11.10 µg/kg and the standard measurement uncertainty as determined in the method validation (um) is 15 %, i.e. 1.67 µg/kg. The difference between analytical result and certified value is therefore 3.2 µg/kg. Prior to the determination of the combined uncertainty, the standard uncertainty of the certified value of the reference material must be determined. The uncertainty of the certified value (UCRM) is given as 95 % confidence interval with 6 degrees of freedom as stated on the certificate. The factor of the t-distribution (t95, 6) is 2.447. The confidence interval must be divided by this factor to obtain the standard uncertainty of the certified value. This standard uncertainty (uCRM) is therefore:
The combined uncertainty (uc) of measurement and certified value is the square root of the quadratic sum of the individual uncertainties:
The results show that the uncertainty of the certified value has almost no influence on the combined uncertainty. This combined uncertainty is now multiplied with a coverage factor of 2 to obtain the expanded uncertainty (here 3.48 µg/kg). This expanded uncertainty is bigger than the difference between analytical results and certified values (3.2 µg/kg). Within the limits of the uncertainties, no method bias is visible.Institutes: