The susceptibility of calibration methods to errors in the analytical signal

Calibration methods differ as to the number and concentration of calibration standards, and whether these are added to the samples or separate from them. The four main calibration mehods (single separate or added standard and multiple separate or added standards) and some modifications are desribed mathematically and subjected to error-propagation analysis, to examine the likely effects of errors in the analytical signal on the overall accuracy and precision of the concentration estimate. Comparison of the results throws light on the influence of the number, concentration and nature of the calibration standards, the effects of sample and standard replication, and the costs and the benefits of blank measurements. It is shown that all standard-addition methods are immune to proportional signal error, but more sensitive to nonlinearity. In separate-standard methods, all bias disappears when the true sample concentration (x_s) is equal to the standard concentration or to the mean standard concentration ($\text{x}$). Only the multiple separate standard method is unaffected by constant error common to sample and standards, without blanking. In multiple-standard methods, precision is best at x_s = $\text{x}$. Precision is always improved by increasing the number of sample and standard measurements; standard-addition methods respond best to sample replication. Whichever calibration method is used, recovery correction will eliminate proportional concentration error, at the cost of decreased precision.