A Step-wise Approach to the Determination of the Lower Limit of Analysis of the Calibration line

Jens Enevold Thaulov Andersen

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A method is presented of stipulating the extension of the calibration line in analytical chemistry. It is based on a combination of a chemometric data interpretation and a calculation of the minimum standard deviation (STDEV) of experiments. From a depiction of the STDEV of a straight line vs. residuals, the more favourable concentration range of calibration could be obtained by iteration using only but 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 STDEV’s on slope and on intercept 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 the 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, as to fulfil the conditions of the central-limit theorem.
Original languageEnglish
JournalJournal of Analytical Chemistry
Issue number4
Pages (from-to)308-319
Publication statusPublished - 2008


  • limit of detection
  • measurement uncertainty
  • Quality assurance


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