A step-wise approach to the determination of the lower limit of analysis of the calibration line

A method is presented of stipulating the extension of the calibration line in analytical chemistry. The method is based on a combination of chemometric data interpretation and the calculation of the minimum standard deviation (STDEV) of experiments. From the depiction of the STDEV of a straight line versus the residuals, the more favorable concentration range of calibration could be obtained by iteration using only a few steps. This condition links the lower limit of analysis (LLA) to an upper limit of analysis (ULA), and, thus, completes the statistically appropriate extension of the calibration line. In addition, a minimum STDEV of measurement was expressed in terms of the STDEV on the slope ( s a ) and on the intercept ( s b ), and the calculation was performed by using a modified version of the law of propagation of errors (LPE). The method was validated on experiments of gas chromatography (GC), liquid chromatography (LC), electrochemistry, flow-injection analysis (FIA), atomic emission spectrometry (AES), flame atomic absorption spectrometry (FAAS), and inductively coupled-plasma mass spectrometry (ICP-MS). A novel definition of the ULA was proposed as the concentration where the response started to deviate significantly from linearity, also taking into account the level of uncertainty. The proposed method facilitates the determination of the concentration range of calibration and LLA in one working operation. In order to promote reliability, it was proposed that the number of repetitions of analysis should be high, preferably above 100, in order to fulfill the conditions of the central-limit theorem.