Objective evaluation of precision requirements for geochemical analysis using robust analysis of variance

The pursuit of high precision in geochemical analysis has no inherent limit. An appropriate analytical precision requirement can be set, however, by comparing the “analytical variance” with the other sources of variance in geochemical data.

The purpose of a geochemical survey is to give a description of the geochemical variation of a region. Numerically this can be expressed in terms of the natural “geochemical variance” of the area. The information content is diminished by the two processes of measurement: the act of taking a sample adds a random error with “sampling variance”; and the act of chemical analysis adds another random error with “analytical variance”.

In order to optimise the analytical variance for cost-effectiveness, rather than simply to minimize it, all three variances must be estimated. This requires that traditional analytical quality control be extended to include the total measurement process, rather than only the “analytical” portion. Such a Sampling and Analytical Quality Control Scheme (SAX) requires some duplication of field samples and the duplicate analysis of each field duplicate. A robust Analysis of Variance (ANOVA) is then used to separate the three components of the total variance. Robust statistics can accommodate outlying values that have undue influence on classical ANOVA.

For a clear description of the natural geochemical variance, the combined sampling and analytical variances for the data should comprise not more than, say, 20% of the total variance. If this figure is exceeded then these extraneous variances should be reduced. The decision as to whether this reduction requires improved sampling or improved analytical precision can also be based on the ANOVA results. As a general rule, we suggest that the analytical variance should comprise not more than 4% of the total variance. If, on the other hand, the analytical variance is less than 1% of the total variance, then needless expense has probably been incurred and the natural geochemical variation can be adequately described with less precise methods of analysis. Similar arguments can be applied to sampling variance.

An application of SAX with robust ANOVA to a stream sediment survey for Cu, Pb and Zn demonstrates the advantages of the technique. For the analytical geochemist it provides a realistic target for analytical precision. For the field geochemist it provides a quantitative tool for the design of geochemical surveys. It facilitates the optimisation of both sampling and chemical analysis for a particular region to reveal geochemical patterns at minimal expense.