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Average Relative Error in Geochemical Determinations: Clarification, Calculation, and a Plea for Consistency

¹ Department of Earth and Environmental Science, Acadia University, Wolfville, Nova Scotia, B4P 2R6; e-mail: cliff.stanley{at}acadiau.ca
² ioGlobal, Level 3, IBM Building, 1060 Hay Street, West Perth, Western Australia, 6005, Australia; e-mail: dave.lawie{at}ioglobal.net

The measurement of error in assays collected as part of a mineral exploration program or mining operation historically has been undertaken in a variety of ways. Different parameters have been used to describe the magnitude of relative error, and each of these parameters is related to the standard measure of relative error, the coefficient of variation. Calculation of the coefficient of variation can be undertaken in a variety of ways; however, only one produces unbiased estimates of measurement error: the root mean square coefficient of variation calculated from the individual coefficients of variation.

Thompson and Howarth’s error analysis approach has also been used to describe measurement error. However, because this approach utilizes a regression line to describe error, it provides a substantially different measure of error than the root mean square coefficient of variation. Furthermore, because regression is used, Thompson and Howarth’s results should only be used for estimating error in individual samples, and not for describing the average error in a data set. As a result, Thompson and Howarth’s results should not be used to determine the magnitudes of component errors introduced during geochemical sampling, preparation, and analysis.

Finally, the standard error on the coefficient of variation is derived, and it is shown that very poor estimates of relative error are obtained from duplicate data. As a result, geoscientists seeking to determine the average relative error in a data set should use a very large number of duplicate samples to make this estimate, particularly if the average relative error is large.

Key Words: Relative error • root mean square • coefficient of variation • quality control • Thompson-Howarth • error analysis • geochemistry

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