Precision in analytical measurements: Expected values and consequences in geochemical analyses

Abstract

Over the years the authors have developed an empirical formula for the relative standard deviation among laboratories (RSD_R, %) as a function of concentration C, expressed as a decimal fraction: RSD_R=2^{(1−0.5log C)}≈2C^(−0.1505). This formula predicts that starting with a concentration of 100% (pure materials; C=1.00), RSD_R will be 2%, increasing by a factor of 2 for each decrease in C of 2 orders of magnitude. It has been a useful guide to acceptable precision in the fields of agricultural, pharmaceutical, and nutritional chemical analysis. It has now been found that this formula is also useful for interpreting the quality of reported analyses of various reference materials available to geochemists. If a ratio is calculated of the found RSD_R value to the RSD_R value calculated from the formula, an easily interpreted limiting parameter is generated. A ratio >2 provides a rational reference point for interpreting the uncertainty of the analytical portion of the total variability of geochemical concentration estimates. Such a high ratio indicates excessive among-laboratories precision, reflecting large systematic errors on the part of one or more laboratories. The formula quantitates the concept of the transformation of the individual systematic errors of the laboratories into the random error of the group.