External Linear Calibration With a Zero Intercept

1a External Linear Calibration With a Zero Intercept 

If the intercept of a linear caUbration Une (R = A + B.Ca ) can be shown to be statisticaUy indistinguishable from zero, the resulting expressions describing inversion of the calibration function are simplified. The confidence limits for the intercept are given by (Aif.V i), where the value of t is chosen at the desired confidence level (e.g., 0.05, two tailed values since we are concerned with both positive and negative deviations from zero), with (n-2) degrees of freedom, and the variance (V ) is given by Equation [8.26]. If these confidence limits include zero then the intercept is accepted as zero to within the chosen 

In this case the calibration is likely to be obtained as a plot of Rj vs Pj (the amount of calibration standard spiked into a fixed mass of blank matrix prior to extraction, cleanup etc.). Then the experimental slope B corresponds to  

This final working equation is a better situation than that summarized in Equation [8.64f] since, although the various volumes still appear explicitly, the ratio of injection volumes (v /V) is likely unity with little or no uncertainty if an HPLC loop injector is used. Moreover, we now must assume only Fa = Fa rather than Fj = 1 the only reason why Fa might not be exactly equal to Fa is that the extraction efficiency Fa for the native analyte in the analytical sample might be less that for the spiked-in standard analyte (Fa ) a result of occlusion effects of some kind, as can happen with some samples (Boyd 1996, Ke 2000). 

The complete or partial cancellation of the recovery factors in Equation [8.65c] is a major advantage but in itself does not provide an estimate of the recovery from the unknown sample (Fa ). However, access to blank matrix does permit straightforward measurement of VJ (and thus a reasonable estimate of Fa ) by comparing responses Ra for a spiked matrix blank with the corresponding response for the extract of a matrix blank that is spiked with the same amount of standard after the extraction and clean-up. Naturally the extract and injection volumes must be the same in the two cases, preferably the same mass of matrix should be extracted, and a sufficient number of rephcates should be analyzed to provide reasonable estimates of statistical uncertainties. 

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