Quality control in the environmental, geological, and geochemical surveys is dependent upon the accuracy of chemical analyses. Analysts collect duplicate sample pairs to estimate the combined uncertainty in the measurements. The differences observed between the duplicate measurements may cause misunderstandings if the manager cannot distinguish between sampling error in the field and analysis error in the laboratory. Sampling error is due to the heterogeneity and sampling process of the site while analysis error is caused by the laboratory preparation and equipment. Duplicate samples are used as the means to identify both errors.
Discrimination between measurement error requires an experimental design with two levels of replication. The field duplicates are independent primary samples taken at the same location using identical methodology and encompassing variation due to spatial heterogeneity, field sampling techniques, and analysis process. The laboratory duplicates are replicates taken from the same field sample but analysed in duplicate under conditions of repeatability to measure analytical variation only.
A QC program employing the use of duplicates involves the use of this design at selected sites that constitute ten percent of all sampling sites or at least eight sites. In a balanced design, both primary field samples are analysed in duplicate in the lab, resulting in four values for each target site.
The unbalanced nested design involves the duplicate analysis of only one of the primary field samples. This unbalanced design saves approximately one-third of laboratory cost, while still retaining proper degrees of freedom. The randomization of all sub-samples ensures unbiased precision estimates.
Variance analysis in general and analysis of variance (ANOVA) in particular serve as the main statistical approach used for splitting the overall data variance into the following additive parts: between-target variance, sampling variance, and analytical variance. Overall uncertainty associated with measurements equals the square root of the sum of sampling and analytical variances. In cases where the distribution is heavily skewed or contains outliers, RANOVA proves useful in that it reduces the weight of such outliers thus preventing the overestimation of population uncertainty. If relative standard deviations reach more than twenty percent or concentrations cover different orders of magnitude, the log-transformation helps in variance stabilization.
There are graphical techniques in addition to ANOVA calculations. The Thompson-Howarth plot serves as a tool for assessing precision within dynamic ranges via plotting absolute differences between two duplicates against average concentration. Calculations of relative percent differences (RPDs) and R-charts serve as a way of establishing upper warning and action limits based on standard deviations.
Empirical studies have proven repeatedly that field sampling variance accounts for most of the measurement uncertainty of natural materials; at times, over seventy to ninety percent of total variance is due to field sampling variance, while analytical errors account for less than ten percent of total uncertainty. A large relative percent difference in field duplicates along with a small relative percent difference in laboratory duplicates indicates sample heterogeneity, a low sample mass, or lack of field sample homogenization, while a large relative percent difference in laboratory duplicates implies instrumentation problems or calibration issues.
A corrective action must focus on addressing the dominant source of error to improve data cost-effectively. Redundant analysis adds to costs but does not help minimize total measurement error since field sampling is the dominant source of uncertainty. Managers can improve the accuracy of data by increasing the size of the primary sample, collecting multi-increment composite samples, or improving field splitting procedures.
The concept of duplicate samples is of immense importance in providing a means for diagnosing whether errors are associated with the sampling process at the field level or in the analytical lab process. Well-designed nested experiment designs help achieve the partitioning of variances through analysis of variance. The measurement uncertainty must be fit for purpose such that it accounts for less than twenty percent of the overall variance in the dataset. Quality control in the field helps avoid wasting resources in re-analysis of uncertainties arising from spatial variability.
