Achieving a more accurate method of standard addition through mathematical improvements

The method of standard addition (MSA) has recently benefited from a popularity boost. In this approach, aliquots from a sample with an unknown analyte concentration are spiked with increasing analyte amounts. When plotting the measured signals against the spiked concentrations, the absolute value of the x-axis intercept is the unknown's concentration. Unfortunately, guidance on the best practices for performing MSA is extremely slim. In this article, we rely on literature, mathematical theory, and in silico simulations to build a framework for optimal accuracy when implementing the MSA approach. Our recommendations are as follows. (i) The highest upspike concentration should be as high as possible without saturating the detector; at least five times the estimated unknown concentration is a good rule of thumb. (ii) Adding measurement replicates should be favored over adding new upspike concentrations. (iii) Upspikes towards the low end of the dynamic range should be favored, insofar as their signal is differentiable from the unknown. (iv) To simplify calculations, coordinate swapping should be performed; i.e. signal measurements (e.g. area, area ratio) are recorded as the x values and spiked concentrations as the y values. (v) In performing the least squares regression, weight is set to 1/variance if three or more replicates are available, otherwise, to 1/(signal)2. (vi) If the confidence interval of the quadratic (b2) parameter includes zero, then a linear model should be used for the regression. Otherwise, a quadratic model should be used. (vii) Measurement uncertainty should be calculated using uncertainty contributors uCRM (uncertainty contributed by the certified reference material, as stated on its certificate of analysis) and uMSA (uncertainty contributed by the MSA procedure, which is the uncertainty of the y-intercept, ub0, when using a coordinate-flipped framework).