Sampling as a source of measurement uncertainty: techniques for quantification and comparison with analytical sources

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Abstract
A tutorial review is presented of current methods for the estimation of measurement uncertainty due to primary sampling. Current terminology used in the description of uncertainty and analytical data quality is reviewed and explained. One basic method for the estimation of uncertainty in sampling is described in detail with a worked example of its application to a test dataset. This method employs the taking of a proportion of samples in duplicate, with the further duplication of chemical analysis on these samples. Robust analysis of variance (ANOVA) is applied to estimate the total measurement uncertainty and also to quantify the contributions to that uncertainty which arise from the processes of primary sampling and chemical analysis. The ANOVA program and test data are available electronically to enable application of the methodology. The assumptions and limitations of this basic method are discussed, including its inability to estimate sampling bias. More sophisticated methods are discussed that include the estimation of the contributions to uncertainty from systematic errors in both sampling and analysis. Other approaches to the estimation of uncertainty from sampling, from both sampling theory and geostatistics are compared with these methods. The comparison is made between sampling and chemical analysis as the two sources of uncertainty, relative to each other, and relative to the overall variance of the measurements. Fitness-for-purpose criteria are given and discussed for the ideal maximum and minimum values of the proportion of the measurement variance to the total variance, and the relative contributions of the sampling and analytical variances.

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