The reversed-axis method to estimate precision in standard additions analysis

The standard additions (SA) method is one of the most important calibration strategies in quantitative chemical analysis. It is a powerful tool to minimize matrix effects and enable precise and accurate determinations. On the other hand, the SA method is time-consuming and cumbersome because it requires the preparation of a calibration curve for each individual sample. Considering the statistical treatment required, the estimation of precision in SA determinations can be as laborious and cumbersome as the experimental procedure itself. In this work, we describe a simple method to quickly estimate standard deviations in SA analyses using the determination of Na and K in biodiesel by flame atomic emission spectrometry (FAES) as a model. By taking analyte concentration as the dependent variable (y-axis), and instrument response as the independent variable (x-axis), the standard deviation of the analyte concentration in the sample is equal to the error in the y-axis intercept of the SA calibration curve. This value can be easily calculated using a simple equation or the regression feature in MS Excel. Standard deviation values calculated using MS Excel and this reversed-axis method are compared to results from the traditional statistical methods of extrapolation and error propagation. In all determinations, the results from the extrapolation, error propagation with covariance, and reversed-axis methods are identical, which demonstrates their equivalence.