Estimating individual uncertainties – making use of all your replicate analysis

High data quality is characterized by good accuracy of measurement results but equally important by a good estimation of data uncertainty (JCGM 100:2008). Using a good estimate of the uncertainty for data analysis might significantly change the data interpretation: Ignoring or underestimating uncertainties projects too high confidence into the measurand values, while overestimation of uncertainties could blur relevant information in the data. The information carried by the data can be exploited best, if the measurement result would be reported as original (not rounded) number accompanied by the values of the measurement uncertainty (Eggen, et al. 2019). This requires methods to calculate or estimate uncertainties for each analytical datum. Including uncertainties as separate values into the data interpretation is especially important if the data set has individual uncertainties, i.e., every data point has a its ‘own’ uncertainty.

Earth scientists need a method of estimating individual uncertainties based on a few multiple measurements. This method should consider the sample materials' characteristics for which the uncertainty should be assessed, e.g. range of potential measurand values, variability in sample material and heterogeneities. It should also allow to model several sources of uncertainties to account for the multi-step measurement procedure. And last but not least, the method should remain affordable and practical, e.g. the method should also be applicable if samples are send to external laboratories.

In this contribution, we present a method to quantify individual uncertainties with respect to the analyte level (Ellison and Williams 2012)[Annex E.5], including uncertainty model component which allows to model Poisson type error, e.g. due to heterogeneities which are typical for samples in the geosciences. Case studies and examples in data science languages are presented to facilitate the implementation.