Calibration graphs, nonlinear

Consequently, the proof of calibration should never be limited to the presentation of a calibration graph and confirmed by the calculation of the correlation coefficient. When raw calibration data are not presented in such a situation, most often a validation study cannot be evaluated. Once again it should be noted that nonlinearity is not a problem. It is not necessary to work within the linear range only. Any other calibration function can be accepted if it is a continuous function. 

Fig. 3.5 Systematic errors in the standard addition method Cx analyte concentration expected when the calibration dependence is nonlinear in the extrapolation region, c i concentration found when the calibration dependence is reconstructed by a linear calibration graph, c 2 concentration found when analyte in a sample is of different chemical form to that of analyte added to the sample...

Option (Valid) presents a graph of relative standard deviation (c.o.v.) versus concentration, with the relative residuals superimposed. This gives a clear overview of the performance to be expected from a linear calibration Signal = A + B Concentration, both in terms of (relative) precision and of accuracy, because only a well-behaved analytical method will show most of the residuals to be inside a narrow trumpet -like curve this trumpet is wide at low concentrations and should narrow down to c.o.v. = 5% and rel. CL = 10%, or thereabouts, at medium to high concentrations. Residuals that are not randomly distributed about the horizontal axis point either to the presence of outliers, nonlinearity, or errors in the preparation of standards. 

Over time, statisticians have devised many tests for the distributions of data, including one that relies on visual inspection of a particular type of graph. Of course, this is no more than the direct visual inspection of the data or of the calibration residuals themselves. However, a statistical test is also available, this is the x2 test for distributions, which we have previously described. This test could be applied to the question, but shares many of the disadvantages of the F-test and other tests. The main difficulty is the practical one this test is very insensitive and therefore requires a large number of samples and a large departure from linearity in order for this test to be able to detect it. Also, like the F-test it is not specific for nonlinearity, false positive indication can also be triggered by other types of defects in the data. 

Having satisfactorily determined elution conditions for a particular compound or group of compounds, calibration curves must then be obtained to ensure the linearity (or lack thereof) of each integrated signal at different concentrations An example of such a calibration curve is shown for Z-comfenn 4 (Fig 9 2 10) as a function of absorbance against concentration As expected, a linear response was noted over the concentrations studied This would not have been the case had the column been overloaded or if nonlinear adsorption had occurred Such graphs are particularly useful when quantification of a particular constituent is required... 

Figure 18 Calibration curves using an internal standard (IS). Analytes are quantified against an IS that has been added as early as possible in the analytical procedure. The ratios of detector responses for the analyte (fiA) and IS (R S) are plotted against the ratio of known amounts of analyte (A) and IS. When a sample is analyzed, the ratio Ra/Ris is measured. Then knowing the amount of IS added into the sample, the amount of analyte present in the sample can be estimated. Curves that do not pass through the origin of the graph or which are nonlinear are diagnostic of (a) chemical interference or sample carryover, (b) sample loss during the assay due to adsorption, and (c) saturation or cross-contribution between the IS and the analyte.

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